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Gühne, Otfried. "Detecting quantum entanglement entanglement witnesses and uncertainty relations /." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972550216.
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Ray, Megan. "Verifying Optical Entanglement." Thesis, University of Oregon, 2013. http://hdl.handle.net/1794/13430.
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We look at the problem of verifying optical entanglement for two types of states relevant to quantum information processing. One type occurs in Hong-Ou-Mandel interference and is relevant to quantum computing. The other type is time frequency entanglement which is useful for quantum key distribution. For these types of states the conventional methods of entanglement verification do not work well, and we develop new criteria and methods to verify entanglement of such states. Explicitly, one method takes into account the possible multimode character of two photons, while the other method takes into account the missing data that occur due to the finite range of detectors.
This dissertation includes previously published and unpublished co-authored material.
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Bae, Joonwoo. "Entanglement and Quantum Cryphtography." Doctoral thesis, Universitat de Barcelona, 2007. http://hdl.handle.net/10803/1589.
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Quantum cryptography is one of the most important quantum information applications. The present thesis covers several topics on quantum cryptography, such as the security analysis of quantum channels for key distribution protocols and the study of quantum cloning.First, we introduce a general formalism to characterize the cryptographic properties of quantum channels in the realistic scenario where the two honest parties employ prepare and measure protocols and the known two-way communication reconciliation techniques. We derive a necessary and sufficient condition to distill a secret key using this type of schemes for arbitrary bipartite quantum systems of finite dimension. The obtained results suggest that there may exist weakly entangling channels useless for key distribution using prepare and measure schemes.
Next, we consider Gaussian states and Gaussian operations for cryptographic tasks and derive a new security condition. As it happens for quantum systems of finite dimension, our results suggest that there may also exist weakly entangled Gaussian states useless for key distribution, using Gaussian operations.
Finally, we study the connection between cloning and state estimation.
It was a long-standing problem to show whether state estimation becomes equivalent to quantum cloning in the asymptotic limit of an infinite number of clones. The equivalence is proven here using two known results in quantum information theory, the monogamy of quantum states and the properties of entanglement-breaking channels.
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Gray, Sean. "Quantum Entanglement and Cryptography." Thesis, Uppsala universitet, Teoretisk fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-227085.
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In this paper the features of quantum systems which lay the foundation of quantum entanglement are studied. General properties of entangled states are discussed, including their entropy and relation to Bell's inequality. Applications of entanglement, namely quantum teleportation and quantum cryptography, are also considered.
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Orús, Lacort Román. "Entanglement, quantum phase transitions and quantum algorithms." Doctoral thesis, Universitat de Barcelona, 2006. http://hdl.handle.net/10803/482202.
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From the seminal ideas of Feynman and until now, quantum information and computation has been a rapidly evolving field. While at the beginning, physicists looked at quantum mechanics as a theoretical framework to describe the fundamental processes that take place in Nature, it was during the 80’s and 90’s that people began to think about the intrinsic quantum behavior of our world as a tool to eventually develop powerful information technologies. As Landauer pointed out, information is physical, so it should not look strange to try to bring together quantum mechanics and information theory. Indeed, it was soon realized that it is possible to use the laws of quantum physics to perform tasks which are unconceivable within the framework of classical physics. For instance, the discovery of quantum teleportation, superdense coding, quantum cryptography, Shor’s factorization algorithm or Grover’s searching algorithm, are some of the remarkable achievements that have attracted the attention of many people, both scientists and non-scientists. This settles down quantum information as a genuine interdisciplinary field, bringing together researchers from different branches of physics, mathematics and engineering.
While until recently it was mostly quantum information science that benefited from other fields, today the tools developed within its framework can be used to study problems of different areas, like quantum many-body physics or quantum field theory. The basic reason behind that is the fact that quantum information develops a detailed study of quantum correlations, or quantum entanglement. Any physical system described by the laws of quantum mechanics can then be considered from the perspective of quantum information by means of entanglement theory.
It is the purpose of this introduction to give some elementary background about basic concepts of quantum information and computation, together with its possible relation to other fields of physics, like quantum many-body physics. We begin by considering the definition of a qubit, and move then towards the definition of entanglement and the convertibility properties of pure states by introducing majorization and the von Neumann entropy. Then, we consider the notions of quantum circuit and quantum adiabatic algorithm, and move towards what is typically understood by a quantum phase transition, briefly sketching how this relates to renormalization and conformal field theory. We also comment briefly on some possible experimental implementations of quantum computersDesde las pioneras ideas de Feynman hasta el día de hoy, la información y computación cuánticas han evolucionado de forma veloz. Siendo la mecánica cuántica en sus orígenes considerada esencialmente como un marco teórico en el que poder explicar ciertos procesos fundamentales que acontecían en la Naturaleza, fue durante los años 80 y 90 cuando se empezó a pensar sobre el comportamiento intrínsecamente cuántico del mundo en el que vivimos como una herramienta con la que poder desarrollar tecnologías de la información más potentes, basadas en los mismos principios de la física cuántica. Tal y como Landauer dijo, la información es física, por lo que no debe en absoluto extrañarnos el que se intentara comulgar la mecánica cuántica con la teoría de la información. Y nada más lejos de la realidad, pues pronto se vio que era posible utilizar las leyes de la física cuántica para realizar tareas inconcebibles desde un punto de vista clásico. Por ejemplo, el descubrimiento de la teleportación, la codificación superdensa, la criptografía cuántica, el algoritmo de factorización de Shor o el algoritmo de búsqueda de Grover, constituyen algunos de los logros remarcables que han atraído la atención de mucha gente, dentro y fuera de la ciencia. Queda la información cuántica, pues, constituida como un campo genuinamente pluridisciplinar, en el que se concentran investigadores provenientes de diferentes ramas de la física, las matemáticas y la ingeniería. Mientras en sus orígenes era la información cuántica quien se beneficiaba del conocimiento de otros campos, a día de hoy las herramientas desarrolladas en el marco de la teoría cuántica de la información pueden ser asimismo usadas en el estudio de problemas de diferentes áreas, como la física de muchos cuerpos o la teoría cuántica de campos. Ello es debido al estudio detallado que la información cuántica desarrolla de las correlaciones cuánticas, o entrelazamiento cuántico. Cualquier sistema físico descrito por las leyes de la mecánica cuántica se puede por lo tanto considerar bajo la perspectiva de la teoría cuántica de la información a través de la teoría del entrelazamiento.
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Uyanik, Kivanc. "Entanglement Measures." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609292/index.pdf.
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Being a puzzling feature of quantum mechanics, entanglement caused many debates since the infancy days of quantum theory. But it is the last two decades that it has started to be seen
as a resource for physical tasks which are not possible or extremely infeasible to be done classically. Popular examples are quantum cryptography - secure communication based on
laws of physics - and quantum computation - an exponential speedup for factoring large integers. On the other hand, with current technological restrictions it seems to be difficult to preserve specific entangled states and to distribute them among distant parties. Therefore a precise measurement of quantum entanglement is necessary. In this thesis, common bipartite
and multipartite entanglement measures in the literature are reviewed. Mathematical definitions, proofs of satisfaction of basic axioms and significant properties for each are given as
far as possible. For Tangle and Geometric Measure of Entanglement, which is a multipartite measure, results of numerical calculations for some specific states are shown.
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Alsina, Leal Daniel. "Multipartite entanglement and quantum algorithms." Doctoral thesis, Universitat de Barcelona, 2017. http://hdl.handle.net/10803/459120.
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Quantum information science has grown from being a very small subfield in the 70s until being one of the most dynamic fields in physics, both in fundamentals and applications. In the theoretical section, perhaps the feature that has attracted most interest is the notion of entanglement, the ghostly relation between particles that dazzled Einstein and has provided fabulous challenges to build a coherent interpretation of quantum mechanics. While not completely solved, we have today learned enough to feel less uneasy with this fundamental problem, and the focus has shifted towards its potential powerful applications. Entanglement is now being studied from different perspectives as a resource for performing information processing tasks.
With bipartite entanglement being largely understood nowadays, many questions remain unanswered in the multipartite case. The first part of this thesis deals with multipartite entanglement in different contexts. In the first chapters it is studied within the whole corresponding Hilbert space, and we investigate several entanglement measures searching for states that maximize them, including violations of Bell inequalities. Later, focus is shifted towards hamiltonians that have entangled ground states, and we investigate entanglement as a way to establish a distance between theories and we study frustration and methods to efficiently solve hamiltonians that exhibit it.
In the practical section, the most promised upcoming technological advance is the advent of quantum computers. In the 90s some quantum algorithms improving the performance of all known classical algorithms for certain problems started to appear, while in the 2000s the first universal computers of few atoms began to be built, allowing implementation of those algorithms in small scales. The D-Wave machine already performs quantum annealing in thousands of qubits, although some controversy over the true quantumness of its internal workings surrounds it. Many countries in the planet are devoting large amounts of money to this field, with the recent European flagship and the involvement of the largest US technological companies giving reasons for optimism.
The second part of this thesis deals with some aspects of quantum computation, starting with the creation of the field of cloud quantum computation with the appearance of the first computer available to the general public through internet, which we have used and analysed extensively. Also small incursions in quantum adiabatic computation and quantum thermodynamics are present in this second part.La informació quàntica ha crescut des d'un petit subcamp als anys setanta fins a esdevenir un dels camps més dinàmics de la física actualment, tant en aspectes fonamentals com en les seves aplicacions. En la secció teòrica, potser la propietat que ha atret més interès és la noció d'entrellaçament, la relació fantasmagòrica entre partícules que va deixar estupefacte Einstein i que ha suposat un enorme desafiament per a construir una interpretació coherent de la mecànica quàntica. Sense estar totalment solucionat, hem après prou per sentir-nos menys incòmodes amb aquest problema fonamental i el focus s'ha desplaçat a les seves aplicacions potencials. L'entrellaçament s'estudia avui en dia des de diferents perspectives com a recurs per realitzar tasques de processament de la informació. L'entrellaçament bipartit està ja molt ben comprès, però en el cas multipartit queden moltes qüestions obertes. La primera part d'aquesta tesi tracta de l'entrellaçament multipartit en diferents contextos. Estudiem l'hiperdeterminant com a mesura d'entrellaçament el cas de 4 qubits, analitzem l'existència i les propietats matemàtiques dels estats absolutament màximament entrellaçats, trobem noves desigualtats de Bell, estudiem l'espectre d'entrellaçament com a mesura de distància entre teories i estudiem xarxes tensorials per tractar eficientment sistemes frustrats. En l'apartat pràctic, el més prometedor avenç tecnològic del camp és l'adveniment dels ordinadors quàntics. La segona part de la tesi tracta d'alguns aspectes de computació quàntica, començant per la creació del camp de la computació quàntica al núvol, amb l'aparició del primer ordinador disponible per al públic general, que hem usat extensament. També fem petites incursions a la computació quàntica adiabàtica i a la termodinàmica quàntica en aquesta segona part
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Tsegaye, Tedros. "Quantum interference, complementarity and entanglement." Doctoral thesis, KTH, Electronic Systems Design, 2000. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3004.
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Nozaki, Masahiro. "Quantum Entanglement of Local Operators." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199101.
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Vedral, Vlatko. "Quantum information theory of entanglement." Thesis, Imperial College London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299786.
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Song, David Daegene. "Manipulating quantum information and entanglement." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365320.
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Henderson, L. "Quantum entanglement and classical information." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365802.
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Campbell, Earl T. "Distrubuting entanglement for quantum computing." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.504315.
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Tang, Wai Ho. "Quantum Entanglement and Superconducting Qubits." Thesis, Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-32238.
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Conventional computing based on classical technologies is approaching its limits. Therefore scientists are starting to consider the applications of quantum mechanics as a means for constructing more powerful computers. After proposing theoretical methods, many experimental setups have been designed to achieve quantum computing in reality. This thesis gives some background information on the subject of quantum computing. We first review the concept of quantum entanglement, which plays a key role in quantum computing, and then we discuss the physics of the SQUIDs-cavity method proposed by Yang et al., and give the definitions of quantum gates which are the elements that are needed to construct quantum circuits. Finally we give an overview of recent developments of SQUIDs-cavity systems and quantum circuits after Yang et al.'s proposal in 2003. These new developments help to take a step towards the constructions of higher levels of quantum technologies, e.g. quantum algorithms and quantum circuits.
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Yuen, Henry Ph D. Massachusetts Institute of Technology. "Games, protocols, and quantum entanglement." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/107364.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 177-184).
Quantum entanglement has evolved from being "spooky action at a distance" to being a fundamental information-theoretic resource, extending the frontiers of what is possible in communications, computation, and cryptography. It gives rise to non-local correlations that can be harnessed to perform tasks such as certified randomness generation and classical verification of quantum computation. However, these same non-local correlations also pose a challenge when analyzing complexity-theoretic or cryptographic protocols in a quantum world: the soundness or security of the protocol may no longer hold in the presence of entangled adversaries. This thesis presents several results involving games and protocols with entangled parties; in each result, we introduce new techniques and methods to analyze soundness against adversaries that can manipulate quantum entanglement. First, we present a protocol wherein a classical verifer interacts with eight non-communicating quantum devices, and for all integer N the verifier can statistically certify that the devices have produced N bits of randomness that is E-close to uniform, while only using O(log³ 1/[epsilon]) bits of seed randomness. We call this an infinite randomness expansion protocol, because the amount N of certified output randomness is independent of the verifier's seed length. Entanglement is both a blessing and a curse for this protocol: on one hand, the devices need entanglement in order to successfully generate randomness to pass the protocol. But on the other hand, the devices may try to use entanglement to cheat and pass the protocol without producing additional randomness. We show that the monogamous nature of entanglement prevents this from happening. Next, this thesis studies the parallel repetition of games with entangled players. Raz's classical parallel repetition theorem (SICOMP 1998) is an influential result in complexity theory showing that the maximum success probability of unentangled players in a two-player game must decrease exponentially when the game is repeated in parallel. Its proof is highly non-trivial, and a major open question is whether it extends to the case of entangled players. We make progress on this question in several ways. First, we present an efficient transformation on games called "anchoring" that converts any k-player game G into a k-player game G[upside down upper case T] such that the entangled value of its n-fold parallel repetition, Gn[upside down upper case T], is exponentially small in n (provided that the entangled value of G is less than 1). Furthermore, the transformation is completeness preserving, in that if the entangled value of G is 1, then the entangled value of Gn[upside down upper case T] is also 1. This yields the first gap amplification procedure for general entangled games that achieves exponential decay. We also show that parallel repetition of a game causes the entangled value to decrease at a polynomial rate with the number of repetitions. In particular, this gives the first proof that the entangled value of a parallel repeated game converges to 0 for all games who entangled value is less than 1. The third result of this thesis on entangled parallel repetition is an improved analysis of the parallel repetition of free games with entangled players. Free games are those where the players' questions are independent of each other. We show how to use the fact that the DISJOINTNESS problem of size N can be solved with O([square root]N) qubits of quantum communication in order to speed up the rate of decay for the parallel repetition: given a free game G with entangled value 1 - [epsilon], its n-fold parallel repetition Gn has entangled value at most (1 - [epsilon]³/²)[omega](n/s), where s is the length of the players' answers in G. In contrast, the best parallel repetition theorem for free games with unentangled players, due to Barak, et al. (RANDOM 2009), shows that for a free game G with entangled value 1 - [delta], the classical value of Gn is at most (1 - [epsilon]² )[omega](n/s), which is a slower rate of decay. This suggests a separation between the behavior of entangled games and unentangled games under parallel repetition. In the final part of this thesis, we examine message authentication in a quantum world. Message authentication is a fundamental task in cryptography that ensures data integrity when communicating over an insecure channel. We consider two settings. One is classical authentication against quantum attacks. The other is total quantum authentication of quantum data. We give a new class of security definitions for both modes of message authentication. Our definitions capture and strengthen several existing definitions, including that of Boneh-Zhandry (EUROCRYPT 2013), which pertains to superposition attacks on classical authentication schemes, as well as the definition of Barnum, et al. (FOCS 2002), which addresses total authentication of quantum data. Our definitions give strong characterizations for what a quantum adversary is able to do in a message authentication protocol, even when the adversary has quantum side information that is entangled with the message state. We argue that, in the "one time" setting, our definitions are the strongest possible. We prove that our security definition for total quantum authentication has some surprising implications, such as the ability to reuse the key whenever verification is successful, and a conceptually simple quantum key distribution protocol. We then give several constructions of protocols that satisfy our security definitions: (1) we show that the classical Wegman-Carter scheme with 3-universal hashing is secure against quantum adversaries with quantum-side information; (2) we present a protocol based on unitary designs that achieves total quantum authentication, and (3) we show that using the classical Wegman- Carter scheme to authenticate in complementary bases yields a form of total quantum authentication, with bounded key leakage.
by Henry Yuen.
Ph. D.
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Timothy, H. Hsieh Timothy (Timothy Hwa-wei). "Topological materials and quantum entanglement." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/103228.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2015.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 83-91).
As the title implies, this thesis consists of two main topics: materials which realize topological phases of matter and applications of the concept of entanglement in understanding topological phases and their transitions. The first part will focus on a particular class of materials called topological crystalline insulators (TCI), which are bulk insulators with metallic boundary states protected by crystal mirror symmetries. The realization of TCIs in the SnTe class of materials and the anti-perovskite family will be described. The second part will focus on using entanglement notions to probe a topological phase transition, based on a single topological wavefunction. This is achieved by performing extensive partitions of the wavefunction, such as a checkerboard partition. Implementing this technique in one dimension naturally involves the use of tensor networks, which will be reviewed and then utilized.
by Timothy H. Hsieh.
Ph. D.
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Parker, Rachel Frances. "Quantum entanglement and fault-tolerance." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615063.
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Lin, Ho-Chih. "Local approach to quantum entanglement." Thesis, University College London (University of London), 2008. http://discovery.ucl.ac.uk/1446283/.
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Quantum entanglement is the key property that makes quantum information theory different from its classical counterpart and is also a valuable physical resource with massive potential for technological applications. However, our understanding of entanglement is still far from com plete despite intense research activities. Like other physical resources, the first step towards exploiting them fully is to know how to quantify. There are many reasons to focus on the en tanglement of continuous-variable states since the underlying degrees of freedom of physical systems carrying quantum information are frequently continuous, rather than discrete. Much of the effort has been concentrated on Gaussian states, because these are common as the ground or thermal states of optical modes. Within this framework, many interesting topics have been stud ied and some significant progress made. Nevertheless, non-Gaussian states are also extremely important this is especially so in condensed-phase systems, where harmonic behaviour in any degree of freedom is likely to be only an approximation. So far, there is little knowledge about the quantification of entanglement in non-Gaussian states. This thesis aims to contribute to the active field of research in quantum entanglement by introducing a new approach to the analysis of entanglement, especially in continuous-variable states, and shows that it leads to the first systematic quantification of the (local) entanglement in arbitrary bipartite non-Gaussian states. By applying this local approach, many new insights can be gained. Notably, local entanglements of systems with smooth wavefunctions are fully characterised by the derived simple expressions, provided the wavefunction is known. The local (logarithmic) negativity of any two-mode mixed states can be directly computed from the closed-form formulae given. For multi-mode mixed states, this approach provides a scheme that permits much simpler numerical computation for quantifying entanglement than is generally possible from directly computing the full entanglement of the system.
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Spedalieri, Federico Maximiliano Preskill John P. "Characterizing entanglement in quantum information /." Diss., Pasadena, Calif. : California Institute of Technology, 2003. http://resolver.caltech.edu/CaltechETD:etd-05222003-121058.
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CAPONIGRO, MICHELE. "Quantum Entanglement: Non-Local Implications." Doctoral thesis, Università degli studi di Bergamo, 2011. http://hdl.handle.net/10446/920.
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Xiong, Han. "Coherence-induced entanglement." Texas A&M University, 2005. http://hdl.handle.net/1969.1/3797.
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Coherence and entanglement are the two key concepts that distinguish quantum
mechanics from classical mechanics. Many novel phenomena occuring in the quantum
world are due to these two Âphysical quantitiesÂ. They also play essential roles in
quantum computation and quantum information. For example, coherence, which
says that a quantum mechanical system could be in a superposition state, makes the
quantum parallel computing scheme possible; and entanglement, which says that two
quantum systems separated in space could be in an intervened state, is the key factor
in various quantum teleportation algorithms.
We have studied entanglement generation in various systems. We found that with
atomic coherence, entanglement could be generated between two thermal fields with
arbitrarily high temperatures. We also found that temperature difference instead of
the purity of state is essential for the entanglement generation between an atom and
a thermal field. We discovered that correlated spontaneous emission lasers (CELs)
could be used to generate bright entanglement laser beams. As a special case of CEL
systems, we studied entanglement generation in Non-degenerate Optical Parametric
Amplifiers (NOPAs). We performed the input-output calculations for a NOPA system
and showed that the two output optical beams are still entangled. This justifies our idea that CEL (or NOPA) systems can be used as an ideal entanglement source
for various quantum information schemes. From an experimental point of view, we
considered the effects of pumping fluctuations on entanglement generation in CEL
and NOPA systems. We found that these fluctuations, especially the phase diffusion
processes, in the pump laser would greatly reduce the entanglement generated in such
systems.
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Lan, Shau-Yu. "Matter-light entanglement with cold." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/28197.
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Thesis (M. S.)--Physics, Georgia Institute of Technology, 2009.Committee Chair: Kuzmich, Alex; Committee Member: Chapman, Michael; Committee Member: Citrin, David; Committee Member: Kennedy, T. A. Brian; Committee Member: Raman, Chandra
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Clarisse, Lieven. "Entanglement distillation : a discourse on bound entanglement in quantum information theory." Thesis, University of York, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434001.
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Di, Tiegang. "Entanglement generation and applications in quantum information." Texas A&M University, 2006. http://hdl.handle.net/1969.1/3840.
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This dissertation consists of three sections. In the first section, we discuss the generation
of arbitrary two-qubit entangled states and present three generation methods.
The first method is based on the interaction of an atom with classical and quantized
cavity fields. The second method is based on the interaction of two coupled two-level
atoms with a laser field. In the last method, we use two spin-1/2 systems which
interact with a tuned radio frequency pulse. Using those methods we have generated
two qubit arbitrary entangled states which is widely used in quantum computing and
quantum information. In the second section, we discuss a possible experimental implementation
of quantum walk which is based on the passage of an atom through a
high-Q cavity. The chirality is determined by the atomic states and the displacement
is characterized by the photon number inside the cavity. Our scheme makes quantum
walk possible in a cavity QED system and the results could be widely used on
quantum computer. In the last section, we investigate the properties of teleporting
an arbitrary superposition of entangled Dicke states of any number of atoms (qubits)
between two distant cavities. We also studied teleporting continuous variables of an
optical field. Teleportation of Dicke states relies on adiabatic passage using multiatom
dark states in each cavity and a conditional detection of photons leaking out of both cavities. In the continuous variables teleportation scheme we first reformulate
the protocol of quantum teleportation of arbitrary input optical field states in
the density matrix form, and established the relation between the P-function of the
input and output states. We then present a condition involving squeeze parameter
and detection efficiency under which the P-function of the output state becomes the
Q function of the input state such that any nonclassical features in the input state
will be eliminated in the teleported state. Based on the research in this section we
have made it possible of arbitrary atomic Dicke states teleportation from one cavity
to another, and this teleortation will play an essential role in quantum communication.
Since quantum properties is so important in quantum communication, the
condition we give in this section to distinguish classical and quantum teleportation is
also important.
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Bose, Sougato. "Entanglement manipulations and applications." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.322037.
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Gunhan, Ali Can. "Environmental Effects On Quantum Geometric Phase And Quantum Entanglement." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12609450/index.pdf.
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We investigate the geometric phase (GP) acquired by the states of a spin-1/2 nucleus which is subject to a static magnetic field. This nucleus as the carrier system of GP,
is taken as coupled to a dissipative environment, so that it evolves non-unitarily. We study the effects of different characteristics of different environments on GP as nucleus
evolves in time. We showed that magnetic field strength is the primary physical parameter that determines the stability of GPits stability decreases as the magnetic field strength increases. (By decrease in stability what we mean is the increase in the time rate of change of GP.) We showed that this decrease can be very rapid, and so it could be impossible to make use of it as a quantum logic gate in quantum information theory (QIT). To see if these behaviors differ in different environments, we analyze the same system for a fixed temperature environment which is under the influence of an electromagnetic field in a squeezed state. We find that the general dependence of GP on magnetic field does not change, but this time the effects are smoother. Namely, increase in magnetic field decreases the stability of GP also for in this environment
but this decrease is slower in comparison with the former case, and furthermore it occurs gradually. As a second problem we examine the entanglement of two atoms, which can be used as a two-qubit system in QIT. The entanglement is induced by an external quantum system. Both two-level atoms are coupled to a third two-level system by dipole-dipole interaction. The two atoms are assumed to be in ordinary vacuum and the third system is taken as influenced by a certain environment. We examined different types of environments. We show that the steady-state bipartite entanglement can be achieved in case the environment is a strongly fluctuating, that is a squeezed-vacuum, while it is not possible for a thermalized environment.
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Riera, Graells Arnau. "Entanglement in Many Body Quantum Systems." Doctoral thesis, Universitat de Barcelona, 2010. http://hdl.handle.net/10803/1600.
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THESIS SUMMARYTEXT:
This thesis is made of two parts. In the first one, the issue of entanglement in many body systems is addressed. The concept of entanglement and some of the recent progress on the study of entropy of entanglement in many body quantum systems are reviewed. Emphasis is placed on the scaling properties of entropy for one-dimensional models at quantum phase transitions.
Then, we focus on the area-law scaling of the entanglement entropy. An explicit computation in arbitrary dimensions of the entanglement entropy of the ground state of a discretized scalar free field theory that shows the expected area law result is also presented. For this system, it is shown that area law scaling is a manifestation of a deeper reordering of the vacuum produced by majorization relations.
To finish this first part, the issue of how simple can a quantum system be such as to give a highly entangled ground state is addressed. In particular, we propose a Hamiltonian of a XX model with a ground state whose entropy scales linearly with the size of the block. It provides a simple example of a one dimensional system of spin-1/2 particles with nearest neighbour interactions that violates area-law for the entanglement entropy.
The second part of this thesis deals with the problem of simulating quantum mechanics for highly entangled systems. Two different approaches to this issue are considered. One consists of using ultra-cold atoms systems as quantum simulators. With this aim, some experimental techniques related to cold atoms that allow to simulate strongly correlated many body quantum systems are reviewed an explicit example of simulation is presented. In particular, we analyze how to achieve a Mott state of Laughlin wave functions in an optical lattice and study the consequences of considering anharmonic corrections to each single site potential expansion that were not taken into account until now.
Finally, a different approach to simulate strongly correlated systems is considered: to use small quantum computers to simulate them. An explicit quantum algorithm that creates the Laughlin state for an arbitrary number of particles n in the case of falling fraction equal to one is presented. We further prove the optimality of the circuit using permutation theory arguments and we compute exactly how entanglement develops along the action of each gate. We also discuss its experimental feasibility decomposing the qudits and the gates in terms of qubits and two qubit-gates as well as the generalization to arbitrary falling fraction.
KEYWORDS: Entanglement, Many body quantum systems, Quantum Information Condensed Matter, Cold atoms, Spin chains, Quantum simulator, Quantum computation.
"Entrellaçament quàntic en sistemes de molts cossos"
TEXT:
Aquesta tesi està composada per dues parts. En la primera, adrecem la qüestió de l'entrellaçament quàntic en els sistemes de molts cossos. Així, introduïm primer el concepte d'entrellaçament i revisem els progressos recents sobre aquest camp. A continuació, ens centrem la llei d'àrea per l'entropia d'entrellaçament i presentem un càlcul explícit d'aquesta entropia per a l'estat fonamental d'un camp escalar no interactuant obtenint la llei d'àrea esperada. Finalment, acabem aquesta part presentant un sistema molt senzill 1-dimensional que tot i tenir interaccions locals mostra una llei de volum per l'entropia.
En la segona part de la tesi tractem el problema de la simulació de sistemes quàntics altament entrellaçats. Considerem dos possibles vies per tractar aquest problema. Una d'elles consisteix en la utilització d'àtoms ultra-freds com a simuladors quàntics. En particular, analitzem un mètode per obtenir un estat producte de funcions d'ona de Laughlin en un xarxa òptica i estudiem les conseqüències de considerar la correcció anharmònica de l'expansió del potencial a cada pou de la xarxa. Finalment, considerem una altra aproximació a la simulació de sistemes fortament correlacionats: utilitzar petits ordinadors quàntics per a simular-los. Per il.lustrar aquest tipus de simulació, presentem un algoritme quàntic que crea un estat de Laughlin per un nombre arbitrari de partícules i en el cas de fracció d'ocupació 1.
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Aschwanden, Manuel. "A classical view of quantum entanglement /." Zürich : ETH, Eidgenössische Technische Hochschule Zürich, Department of Information, 2005. http://e-collection.ethbib.ethz.ch/show?type=dipl&nr=179.
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Wellens, Thomas. "Entanglement and control of quantum states." Diss., [S.l.] : [s.n.], 2002. http://edoc.ub.uni-muenchen.de/archive/00000081.
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Cuquet, Palau Martí. "Entanglement distribution in quantum complex networks." Doctoral thesis, Universitat Autònoma de Barcelona, 2012. http://hdl.handle.net/10803/107850.
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Aquesta tesi tracta l’estudi de xarxes quàntiques amb una estructura complexa, les implicacions que aquesta estructura té en la distribució d’entrellaçament i com el seu funcionament pot ser millorat mitjançant operacions en el règim quàntic. Primer considerem xarxes complexes d’estats bipartits, tant purs com mescla, i estudiem la distribució d’entrellaçament a llargues distàncies. Després passem a analitzar xarxes de canals sorollosos i estudiem la creació i distribució de grans estats multipartits.
El treball contingut en aquesta tesi està motivat principalment per la idea que la interacció entre la informació quàntica i les xarxes complexes pot donar lloc a una nova comprensió i caracterització dels sistemes naturals. Les xarxes complexes tenen una importància particular en les infraestructures de comunicació, ja que la majoria de xarxes de telecomunicació tenen una estructura complexa. En el cas de xarxes quàntiques, que són el marc necessari per al processament distribuït d’informació i comunicació quàntica, és ben possible que en el futur adquireixin una topologia complexa semblant a la de les xarxes existents, o que fins i tot es desenvolupin mètodes per a utilitzar les infraestructures actuals en el règim quàntic.
Una tasca central en les xarxes quàntiques és dissenyar estratègies per distribuir entrellaçament entre els seus nodes. En la primera part d’aquesta tesi, considerem la distribució d’entrellaçament bipartit com un procés de percolació d’entrellaçament en una xarxa complexa. Des d’aquest enfocament, s’estableix entrellaçament perfecte de manera probabilística entre dos nodes arbitraris. Veiem que, per a xarxes grans, la probabilitat d’aconseguir-ho és una constant estrictament major que zero (i independent de la mida de la xarxa) si la quantitat inicial d’entrellaçament està per sobre d’un cert valor crític. La mecànica quàntica ofereix aquí la possibilitat de canviar l’estructura de la xarxa sense necessitat d’establir nous canals “físics”. Mitjançant una transformació local adequada de la xarxa, es pot disminuir l’entrellaçament crític i augmentar la probabilitat. Apliquem aquesta transformació a models de xarxes complexes amb una distribució de graus arbitrària.
En el cas de xarxes sorolloses d’estats mescla, veiem que per algunes classes d’estat es pot utilitzar el mateix enfocament de percolació d’entrellaçament. Per a estats mescla generals considerem una percolació de llargada de camí limitada per la quantitat de soroll de les connexions. Veiem com les xarxes complexes ofereixen encara un gran avantatge en la probabilitat de connectar dos nodes.
En la segona part, passem a l’escenari multipartit. Estudiem la creació i distribució d’estats graf amb una estructura que imita la de la xarxa de comuicació subjacent. En aquest cas, utilitzem una xarxa complexa arbitrària amb canals sorollosos, i considerem que les operacions i mesures són també sorolloses. Proposem un mètode eficient per a distribuir i purificar petits subgrafs, que després es fusionen per a reproduir l’estat desitjat. Comparem aquest enfocament amb dos protocols bipartits basats en un node central i coneixement complet de l’estructura de la xarxa. Mostrem que la fidelitat dels estats graf generats es pot escriure com la funció de partició d’un sistema desordenat de spins clàssics (un vidre de spins), i la seva taxa de decaïment és l’anàleg de l’energia lliure. Utilitzant els tres protocols en una xarxa unidimensional i en xarxes complexes veiem que són tots comparables, i que en alguns casos el protocol de subgrafs proposat, que necessita només informació local de la xarxa, té inclús un comportament millor.This thesis deals with the study of quantum networks with a complex structure, the implications this structure has in the distribution of entanglement and how their functioning can be enhanced by operating in the quantum regime. We first consider a complex network of bipartite states, both pure and mixed, and study the distribution of long-distance entanglement. Then, we move to a network with noisy channels and study the creation and distribution of large, multipartite states. The work contained in this thesis is primarily motivated by the idea that the interplay between quantum information and complex networks may give rise to a new understanding and characterization of natural systems. Complex networks are of particular importance in communication infrastructures, as most present telecommunication networks have a complex structure. In the case of quantum networks, which are the necessary framework for distributed quantum processing and for quantum communication, it is very plausible that in the future they acquire a complex topology resembling that of existing networks, or even that methods will be developed to use current infrastructures in the quantum regime. A central task in quantum networks is to devise strategies to distribute entanglement among its nodes. In the first part of this thesis, we consider the distribution of bipartite entanglement as an entanglement percolation process in a complex network. Within this approach, perfect entanglement is established probabilistically between two arbitrary nodes. We see that for large networks, the probability of doing so is a constant strictly greater than zero (and independent of the size of the network) if the initial amount of entanglement is above a certain critical value. Quantum mechanics offer here the possibility to change the structure of the network without need to establish new, "physical" channels. By a proper local transformation of the network, the critical entanglement can be decreased and the probability increased. We apply this transformation to complex network models with arbitrary degree distribution. In the case of a noisy network of mixed states, we see that for some classes of states, the same approach of entanglement percolation can be used. For general mixed states, we consider a limited-path-length entanglement percolation constrained by the amount of noise in the connections. We see how complex networks still offer a great advantage in the probability of connecting two nodes. In the second part, we move to the multipartite scenario. We study the creation and distribution of graph states with a structure that mimic the underlying communication network. In this case, we use an arbitrary complex network of noisy channels, and consider that operations and measurements are also noisy. We propose an efficient scheme to distribute and purify small subgraphs, which are then merged to reproduce the desired state. We compare this approach with two bipartite protocols that rely on a central station and full knowledge of the network structure. We show that the fidelity of the generated graphs can be written as the partition function of a classical disordered spin system (a spin glass), and its decay rate is the analog of the free energy. Applying the three protocols to a one-dimensional network and to complex networks, we see that they are all comparable, and in some cases the proposed subgraph protocol, which needs only local information of the network, performs even better.
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Gul, Yusuf. "Entanglement Transformations And Quantum Error Correction." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/2/12610773/index.pdf.
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The main subject of this thesis is the investigation of the transformations of pure
multipartite entangled states having Schmidt rank 2 by using only local operations
assisted with classical communications (LOCC). A new parameterization is used for
describing the entangled state of p particles distributed to p distant, spatially separated
persons. Product, bipartite and truly multipartite states are identified in this new
parametrization. Moreover, alternative parameterizations of local operations carried
out by each party are provided. For the case of a deterministic transformation to
a truly multipartite final state, one can find an analytic expression that determines
whether such a transformation is possible. In this case, a chain of measurements by
each party for carrying out the transformation is found. It can also be seen that,
under deterministic LOCC transformations, there are some quantities that remain
invariant. For the purpose of applying the results of this thesis in the context of the
quantum information and computation, brief reviews of the entanglement purification,
measurement based quantum computation and quantum codes are given.
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Yakaboylu, Enderalp. "Entanglement In The Relativistic Quantum Mechanics." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12611487/index.pdf.
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In this thesis, entanglement under fully relativistic settings are discussed. The thesis starts with a brief review of the relativistic quantum mechanics. In order to describe the effects of Lorentz transformations on the entangled states, quantum mechanics and special relativity are merged by construction of the unitary irreducible representations of Poincarégroup on the infinite dimensional Hilbert space of state vectors. In this framework, the issue of finding the unitary irreducible representations of Poincaré
group is reduced to that of the little group. Wigner rotation for the massive particles plays a crucial role due to its effect on the spin polarization directions. Furthermore, the physical requirements for constructing the correct relativistic spin operator is also studied. Then, the entanglement and Bell type inequalities are reviewed. The special attention has been devoted to two historical papers, by EPR in 1935 and by J.S. Bell in 1964. The main part of the thesis is based on the Lorentz transformation of the Bell states and the Bell inequalities on these transformed states. It is shown that entanglement is a Lorentz invariant quantity. That is, no inertial observer can see the entangled state as a separable one. However, it was shown that the Bell inequality may be satisfied for the Wigner angle dependent transformed entangled states. Since the Wigner rotation changes the spin polarization direction with the increased velocity, initial dichotomous operators can satisfy the Bell inequality for those states. By choosing the dichotomous operators taking into consideration the Wigner angle, it is always possible to show that Bell type inequalities can be violated for the transformed entangled states.
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Zander, Claudia. "Information measures, entanglement and quantum evolution." Diss., University of Pretoria, 2007. http://upetd.up.ac.za/thesis/available/etd-04212008-090506.
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Gustavsson, Anna. "Entanglement, nonlinearity and constrained quantum dynamics." Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.512059.
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Abolfathe, Beikidezfuli Salman. "Quantum proof systems and entanglement theory." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/50594.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.Includes bibliographical references (p. 99-106).
Quantum complexity theory is important from the point of view of not only theory of computation but also quantum information theory. In particular, quantum multi-prover interactive proof systems are defined based on complexity theory notions, while their characterization can be formulated using LOCC operations. On the other hand, the main resource in quantum information theory is entanglement, which can be considered as a monotonic decreasing quantity under LOCC maps. Indeed, any result in quantum proof systems can be translated to entanglement theory, and vice versa. In this thesis I mostly focus on quantum Merlin-Arthur games as a proof system in quantum complexity theory. I present a new complete problem for the complexity class QMA. I also show that computing both the Holevo capacity and the minimum output entropy of quantum channels are NP-hard. Then I move to the multiple-Merlin-Arthur games and show that assuming some additivity conjecture for entanglement of formation, we can amplify the gap in QMA(2) protocols. Based on the same assumption, I show that the QMA(k)-hierarchy collapses to QMA(2). I also prove that QMAlog(2), which is defined the same as QMA(2) except that the size of witnesses is logarithmic, with the gap n-(3+e) contains NP. Finally, motivated by the previous results, I show that the positive partial transpose test gives no bound on the trace distance of a given bipartite state from the set of separable states.
by Salman Abolfathe Beikidezfuli.
Ph.D.
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Wang, Xiaoting. "Controlling quantum dynamics and entanglement generation." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609338.
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Bianchini, D. "Entanglement entropy in integrable quantum systems." Thesis, City, University of London, 2016. http://openaccess.city.ac.uk/17490/.
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In this thesis I present the results I have been developing during my PhD studies at City University London. The original results are based on D Bianchini et al, D Bianchini, O Castro-Alvaredo and B Doyon, D Bianchini and F Ravanini, D Bianchini et al and D Bianchini and O Castro-Alvaredo. In all but one publications, we compute the entanglement of various systems. Using the celebrated “replica trick” we compute the entanglement entropy of non unitary systems using integrable tools in continuum and discrete models. In particular, in the first article we generalise the method described in the seventh article in order to take into account non unitary conformal systems. In the second article we use a form factor expansion to probe a non unitary system outside the critical point. In the fourth article we derive the explicit expressions of one dimensional quantum Hamiltonians which provide a lattice realisation of off critical non unitary minimal models. Using a Corner Transfer Matrix approach we compute the scaling of the entanglement of such spin chains. In the fifth article we study the scaling of various twist field correlation functions in order to compute the entanglement entropy and the logarithmic negativity in free boson massive theories.
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Woldekristos, Habtom G. "Tripartite Entanglement in Quantum Open Systems." Miami University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=miami1250185666.
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Saideh, Ibrahim. "Entanglement in high dimensional quantum systems." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS198/document.
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La détection de l’intrication est une étape indispensable dans le contexte de l’information et du calcul quantique. Cette tâche importante s’est avérée difficile pour les systèmes quantiques de grandes dimensions supérieures à 2 × 3, auquel cas il existe des conditions nécessaires et suffisantes bien établies.Notre approche consiste à réduire la dimensionalité du problème. Pour ce faire, on transforme, localement, chaque sous-système en un qubit sans créer de l’intrication. Le mapping est exprimé en fonction des valeurs moyennes de trois opérateurs arbitraires dans l’état original. Nous donnons des conditions nécessaires et suffisantes pour que cette transformation soit valide d'un point de vue physique. Nous exploitons ce formalisme pour dériver des critères d’intrication pour des systèmes bipartites ou multipartites sur la base des critères existants pour les qubits.En transformant localement chaque sous-système, l’application de critères d’intrication connus pour les qubits à l’état résultant induit automatiquement des critères d’intrication en fonction d’opérateurs utilisés pour réaliser le mapping.Pour le cas multipartite, on s’intéresse aux inégalités de compression de spin. Cependant, lorsqu’on applique notre formalisme à ce cas, il est possible d’obtenir une superposition cohérente d’états avec un nombre de particules différent. Par conséquent, pour obtenir de meilleurs critères, nous avons dû prendre en compte les fluctuations quantiques et/ou classiques que l’opérateur du nombre de particules peut présenter. Nous avons dérivé une forme généralisée des inégalités de spin squeezing pour un nombre de particules fluctuant et opérateurs collectifs arbitraires. Nous avons appliqué nos résultats à un système d’atomes de chrome ultrafroids piégés dans un réseau optique, en collaboration avec l’équipe Gazes Dipolaires Quantiques du Laboratoire LPL de l’Université Paris Nord 13. Nous avons montré, dans une simulation numérique, que nos inégalités généralisées sont capables de détecter l’intrication à l’aide d’opérateurs collectifs mesurables en utilisant des techniques accessibles dans dans ce type de dispositifEntanglement detection is crucial and a necessity in the context of quantum information and quantum computation. This important task has proved to be quite hard for quantum systems of dimensions higher than 2×3, in which case, there exists well established necessary and sufficient conditions like Peres-Horodecki criterion.To tackle this challenge for bipartite systems, we introduce a mathematical framework to reduce the problem to entanglement in a two qubit system. This is done by mapping each subsystem locally into a qubit without increasing entanglement. The mapping is expressed in terms of expectation values of three arbitrary operators in the original state. We give necessary and sufficient conditions for such mapping to be valid from physical point of view, providing thence a versatile tool for dimension reduction in various applications.Our main use of this formalism is as a gate way to derive entanglement criteria for bipartite or multi-partite systemas based on existing ones derived for qubit systems. By mapping each subsystem locally into a qubit, applying entanglement criteria known for qubits on the resulting state automatically gives us entanglement criteria in terms of the chosen operators used to implement the mapping.For the multi-partite case, we focus on spin squeezing inequalities for qubits to derive entanglement criteria for general systems. However, when applying our formalism to this case, an interesting situation arises where one is able to obtain coherent superposition of multi-partite qubit states with different particle number. Hence, to derive better entanglement criteria, we had to consider quantum and/or classical fluctuationsthat may be exhibited by the particle number operator. We derive generalized form of Sørensen-Mølmer’s criterion and of spin squeezing inequalities for fluctuating particle number in terms of arbitrary collective operators. We applied our results to study entanglement in a system of ultra-cold Chromium atoms with spin s = 3 trapped in a bi-dimensional optical lattice incollaboration with Quantum Dipolar Gazes team in Laboratoire de Physique de Laser at Paris Nord 13 university. We showed, in a numerical simulation, that our generalized inequalities are able to detect entanglement in their system using collective operators. Moreover, we show that such observables can be measured using available techniques
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Liguori, Alexandra Magdalene. "Quantum Markovian dynamics and bipartite entanglement." Doctoral thesis, Università degli studi di Trieste, 2010. http://hdl.handle.net/10077/3583.
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2008/2009In questa tesi di dottorato si sono studiati i cosiddetti sistemi quantistici aperti, cioè sistemi sici la cui interazione con l'ambiente esterno non può essere trascurata, da due prospettive: da un lato si sono caratterizzate le proprietà del bagno mediante grandezze siche del sottosistema immerso in esso; dall'altro si è studiato l' entanglement, dal punto di vista sia della sua generazione sia della sua evoluzione temporale, in sistemi bipartiti immersi e interagenti con un bagno esterno. La mia tesi di dottorato, Quantum Markovian Dynamics and Bipartite En- tanglement (Dinamica Markoviana quantistica ed entanglement bipartito ) è organizzata nel seguente modo. Nel primo capitolo vengono descritti brevemente i sistemi quantistici composti, con particolare attenzione ai sistemi bipartiti, cioè composti da due sottosistemi. Poi si de niscono stati entangled e separabili (non entangled) e vengono illustrati dei criteri di separabilità basati sulle cosiddette mappe positive non completamente positive. In ne, vengono de nite le misure di entanglement e presentati degli esempi di misure importanti. Nel secondo capitolo vengono descritti i sistemi quantistici aperti: innanzitutto vengono de nite le dinamiche reversibili ed irreversibili; poi vengono derivate la dinanica ridotta di un sistema immerso in un bagno esterno con cui interagisce e la rispettiva master equation, spiegando le principali approssimazioni Markoviane in dettaglio. Si considera, in ne, la derivazione degli stati asintotici, con particolare attenzione ai sistemi a uno o due qubit, che sono di interesse per questa tesi. Il terzo capitolo è dedicato alla determinazione dei parametri fenomenologici della master equation in un particolare sistema quantistico aperto unidimensionale. Questo sistema è costituito da un lo in cui è ssata un'impurezza di spin 1=2 la quale interagisce magneticamente con un elettrone che può propagarsi lungo suddetto lo. L'intero sistema è immerso in un bagno esterno i cui e etti di dissipazione e rumore agiscono solo sul grado di libertà di spin dell'impurezza. Per questo sistema vengono trovate delle espressioni esplicite per i parametri del rumore dovuti all'ambiente in termini delle probabilità di trasmissione e ri essione dell'elettrone, che si possono misurare. Nel quarto capitolo viene descritto il comportamento dell'entanglement in sistemi quantistici aperti: in particolare viene studiato un sistema composto da due qubits e si analizzano sia le condizioni di generazione di entanglement in uno stato inizialmente separabile sia la possibilità che questo entanglement persista nello stato asintotico. In ne, gli ultimi due capitoli trattano esempi espliciti del comportamento dell' entanglement in sistemi quantistici aperti, da un lato, nel Capitolo 5, analizzando la generazione di entanglement, dall'altro, nel Capitolo 6, descrivendo l'evoluzione temporale dell'entanglement e confrontandola con quella dell'entropia. Nel quinto capitolo, viene considerato un sistema bipartito di due qubits immersi in un bagno esterno comune col quale interagiscono debolemente (senza interagire direttamente tra di loro) e viene trovata una condizione necessaria e su ciente a nchè venga generato entanglement, solo tramite l'azione del bagno, in uno stato inizialmente separabile dei due qubits. Poi questa condizione viene generalizzata ad una condizione su ciente per la generazione di entanglement tramite il bagno in sistemi bipartiti di dimensione arbitraria. Nel sesto capitolo, si considera di nuovo un sistema bipartito composto di due qubits immersi in un bagno esterno comune e che evolvono secondo una particolare dinamica dissipativa. In un lavoro precedente era stato congetturato che, per sistemi quantistici aperti senza una Hamiltoniana di interazione esterna, la variazione nel tempo dell' entanglement fosse sempre minore della variazione nel tempo dell'entropia. Quindi, in questo capitolo, si sono studiate le variazioni nel tempo dell'entanglement e dell'entropia per la particolare dinamica dissipativa di nostro interesse. Variando gli stati iniziali del nostro sistema e i parametri del rumore per la nostra evoluzione dissipativa, abbiamo da un lato analizzato il comportamento temporale dell' entanglement e dall'altro paragonato la variazione temporale di quest'ultimo con la variazione temporale dell'entropia. Abbiamo quindi potuto formulare una nuova congettura, basata su una gamma più ampia di esempi: dai nostri risultati si trova che la precedente congettura è veri cata solo se lo stato asintotico della dinamica è separabile, mentre non lo è se lo stato asintotico è entangled.
XXII Ciclo
1981
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De, Chiara Gabriele. "Quantum information, entanglement and critical phenomena." Doctoral thesis, Scuola Normale Superiore, 2006. http://hdl.handle.net/11384/85888.
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Broadfoot, Stuart Graham. "Long distance entanglement distribution." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e7039911-f16b-4f49-8aab-8bb30ae97daa.
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Developments in the interdisciplinary field of quantum information open up previously impossible abilities in the realms of information processing and communication. Quantum entanglement has emerged as one property of quantum systems that acts as a resource for quantum information processing and, in particular, enables teleportation and secure cryptography. Therefore, the creation of entangled resources is of key importance for the application of these technologies. Despite a great deal of research the efficient creation of entanglement over long distances is limited by inevitable noise. This problem can be overcome by creating entanglement between nodes in a network and then performing operations to distribute the entanglement over a long distance. This thesis contributes to the field of entanglement distribution within such quantum networks. Entanglement distribution has been extensively studied for one-dimensional networks resulting in "quantum repeater" protocols. However, little work has been done on higher dimensional networks. In these networks a fundamentally different scaling, called "long distance entanglement distribution", can appear between the resources and the distance separating the systems to be entangled. I reveal protocols that enable long distance entanglement distribution for quantum networks composed of mixed state and give a few limitations to the capabilities of entanglement distribution. To aid in the implementation of all entanglement distribution protocols I finish by introducing a new system, composed of an optical nanofibre coupled to a carbon nanotube, that may enable new forms of photo-detectors and quantum memories.
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Loukopoulos, Klearchos. "Multi-partite entanglement in quantum information processing." Thesis, University of Oxford, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.559825.
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Quantum theories have had an unprecedented success in providing a framework for studying physical systems. A fundamental implication of these theories is the existence of so-called entangled states, that is states whose description cannot be reduced to their constituents. These states are purely quantum and there is no such analogue in classical physics, where knowing the state of every particle is sufficient to infer the state of the system they compose. Entanglement is a core element of many quantum algorithms, quantum teleportation, quantum communications and quantum cryptographic scenarios. Furthermore, entanglement is present in nearly all solid-state systems, when they are at, or close to, their state of lowest energy. Therefore, it is both a technological resource and also a property which needs to be investigated in order to achieve understanding of real world materials at a fundamental level. The most concise demonstration of entanglement is perhaps in the case of maximal entanglement between two spin-l/2 particles. These maximally entangled two- particle states are called Bell states and they have been used to demonstrate experimentally that quantum mechanics is inequivalent to classical mechanics. A gen- eralization of this setting comes from studying entanglement between two physical systems, these can be either pure or mixed (e.g. in contact with a thermal bath). Entanglement between two systems, also knows as bipartite entanglement, has been studied in depth and quantified through various measures. However bipartite entanglement, by definition, is not the only quantity of in- terest. In some cases, entanglement is global and its properties cannot be reduced to studying bi-partitions. This type of entanglement, so-called multipartite entanglement, is harder to quantify and to study in general. Its presence is profound in physical systems that are at the point of undergoing a quantum phase transition and it is also a core ingredient for quantum error correcting codes, performing classical computation with quantum resources and some cryptographic scenarios. In this thesis we study properties of systems with multi-partite entanglement in the context of renormalization and quantum phase transitions, we show that multi- partite entanglement can be used to perform cryptographic tasks and we investigate what classes of Hamiltonians generate multiartite entanglement, while at the same time, their action can be simulated efficiently by a classical computer.
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Jones, Steven. "Verifying Entanglement of Constrained Bipartite Quantum Systems." Thesis, Griffith University, 2009. http://hdl.handle.net/10072/366459.
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Microscopic physical systems requiring a quantum description are increasingly being harnessed to develop useful technologies. The appeal of such an approach lies in the fact that quantum systems possess inherently different properties from those observed on a macroscopic scale. Uniquely quantum phenomena, such as entanglement, offer new tools for performing experimental tasks. For instance, the use of quantum systems for implementing cryptographic protocols and performing computation has caused significant excitement in recent years as it seems likely that the quantum approach offers an advantage over purely classical implementations.
The development of quantum technologies leads to the concept of quantum resources. One key quantum resource that lies at the heart of the divergence between quantum and classical descriptions is that of entanglement. However, for entanglement to act as a resource, it must be possible for the parties (we will restrict ourselves to only two) sharing the entanglement to verify its presence. This may seem like a simple task, however, verifying the properties of quantum systems can be nontrivial. To make matters more complicated, there are often constraints under which the parties sharing the quantum systems find themselves which further restrict the ability of the quantum systems to act as a resource.
One family of constraints arises when the two parties are dealing with quantum systems which have properties constrained by a conservation law, or some other constraint which limits knowledge of the properties of the local subsystems. These constraints can be expressed using the well studied formalism of superselection rules. When a superselection rule applies to quantum systems it can be ambiguous as to whether entanglement survives between the systems. This thesis considers a situation that arises naturally in a nuclear magnetic resonance experiment where two parties share many copies of identical quantum systems. In this case a superselection rule associated with the finite symmetric group applies due to the indistinguishability of the systems. The concept of a reference frame for the symmetric group is used to alleviate the effect of the superselection rule and demonstrate when entanglement survives despite the constraint of indistinguishability. In addition to this, a situation which goes beyond the superselection formalism is considered, one where the operations performable by the two parties are further constrained. It is shown that despite this stronger constraint, it is still possible in principle to verify the existence of entanglement experimentally as demonstrated by the violation of a Bell inequality.
Methods for verifying the presence of entanglement can also prove useful in characterising the properties of entangled quantum systems. Such characterisation may offer insight into the possible advantages offered by quantum systems over their classical counterparts. It becomes possible to more accurately characterise entangled systems by considering a conceptual constraint under which the two parties may find themselves. This is the situation that arises when one of the parties, say Bob, distrusts the other, Alice. In this situation, Alice can only convince Bob of the presence of their entanglement if the entangled system they share possesses a certain property. We term this property steerability, after Schrödinger’s term “steering” [Proc. Camb. Phil. Soc. 31, 553 (1935)] for the Einstein-Podolsky-Rosen effect. This thesis offers a rigorous characterisation of steering in a quantum information context and probes a number of questions relating to this property. First, a number of examples are presented which demonstrate state steerability which is a uniquely quantum property possessed by certain entangled states. Second, the task of experimentally detecting steerability, and thus entanglement, is addressed through the introduction of steerability criteria. Finally two more detailed examples are explored which illustrate various aspects of the measurement dependence of steerability in realistic experiments.Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Biomolecular and Physical Sciences
Faculty of Science, Environment, Engineering and Technology
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Carteret, Hilary Ann. "Symmetry and multiparticle entanglement." Thesis, University of York, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341118.
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Zadra, Federico. "On the quantum entanglement: a geometrical perspective." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17096/.
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Nella tesi viene affrontato il problema dell'entanglement da un punto di vista geometrico, usando sia la geometria differenziale che la geometria algebrica. Particolare attenzione viene data al problema della separabilità: ovvero il distinguere se uno stato è entangled o separabile.
Nel primo capitolo si introduce il formalismo geometrico che verrà usato per analizzare la struttura della meccanica quantistica e dell'entanglement: vengono presentati elementi di geometria differenziale complessa, geometria proiettiva e geometria algebrica.
Nel secondo capitolo, dopo un breve riepilogo sulla meccanica quantistica, vengono usati gli strumenti introdotti nel capitolo precedente per costruirne ed analizzarne la struttura differenziale.
Nel terzo capitolo l'entanglement viene studiato con alcuni esempi ed applicazioni con metodo tradizionale, dopo di che anche gli aspetti geometrici vengono analizzati.
Infine, nell'ultimo capitolo viene proposto un nuovo approccio di tipo algebrico derivato dalla dualità di Schur - Weyl.
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Weber, Markus. "Quantum optical experiments towards atom-photon entanglement." Diss., lmu, 2005. http://nbn-resolving.de/urn:nbn:de:bvb:19-37985.
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Kamat, Angad Mohandas. "Improvements in communication complexity using quantum entanglement." Texas A&M University, 2008. http://hdl.handle.net/1969.1/86008.
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Quantum computing resources have been known to provide speed-ups in computational complexity in many algorithms. The impact of these resources in communication, however, has not attracted much attention. We investigate the impact of
quantum entanglement on communication complexity. We provide a positive result,
by presenting a class of multi-party communication problems wherein the presence of
a suitable quantum entanglement lowers the classical communication complexity. We
show that, in evaluating certains function whose parameters are distributed among
various parties, the presence of prior entanglement can help in reducing the required
communication. We also present an outline of realizing the required entanglement
through optical photon quantum computing. We also suggest the possible impact of
our results on network information flow problems, by showing an instance of a lower
bound which can be broken by adding limited power to the communication model.
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Feller, Alexandre. "Entanglement and Decoherence in Loop Quantum Gravity." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEN058/document.
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Une théorie de gravitation quantique propose de décrire l'interaction gravitationnelle à toutes les échelles de distance et d'énergie. Cependant, comprendre l'émergence de notre espace-temps classique reste un problème toujours ouvert. Cette thèse s'y attaque en gravité quantique à boucles à partir d'outils de l'information quantique.Ceci est fait en plusieurs étapes. La gravité quantique à boucles étant toujours une théorie en cours de développement, un point de vue pragmatique est adopté en étudiant une classe d'état physique du champ gravitationnel, motivée à la fois par des intuitions simples et les résultats de la physique à N corps. Une analyse de la reconstruction de la géométrie à partir des corrélations peut être faite et des leçons peuvent être tirées sur la forme de la dynamique fondamentale. Dans un second temps, la physique des sous-systèmes est analysée en commençant d'abord par évaluer l'entropie d'intrication entre l'intérieur et l'extérieur de la région, permettant ainsi de retrouver la loi holographique de l'entropie des trous noirs et donnant une forme possible des états holographiques de la théorie. Plusieurs dynamiques de la frontière, vu comme un système isolé ou ouvert, sont ensuite analysées, éclairant de nouveau la forme de la dynamique fondamentale. Enfin, la dernière étape de ces recherches étudie la dynamique de la frontière en interaction avec un environnement formé des degrés de liberté (de matière ou gravitationnels) formant le reste de l'Univers et la décohérence sur la frontière qu'il induit. Ceci permet de discuter la transition quantique/classique et de mettre en lumière, dans un modèle donné, les états pointeurs de la géométrieA quantum theory of gravitation aims at describing the gravitational interaction at every scales of energy and distance. However, understanding the emergence of our classical spacetime is still an open issue in many proposals. This thesis analyzes this problem in loop quantum gravity with tools borrowed from quantum information theory.This is done in several steps. Since loop quantum gravity is still under construction, a pragmatic point of view is advocated and an ansazt for physical states of the gravitational field is studied at first, motivated from condensed matter physics and simple intuitions. We analyze the proposal of reconstructing geometry from correlations. Lessons on the quantum dynamics and the Hamiltonian constraint are extracted. The second aspect of this work focuses on the physics of sub-systems and especially the physics of their boundary. We begin by calculating the entanglement entropy between the interior and the exterior of the region, recovering the holographic law known from classical black hole physics. Then different boundary dynamics are studied, both in the isolated and open cases, which shed lights again on the fundamental dynamics. Finally, the last aspect of this research studies the dynamics of the boundary interacting with an environment whose degrees of freedom (gravitational or matter) forming the rest of the Universe and especially the decoherence it induces. This allows to discuss the quantum to classical transition and understand, in a given model, the pointer states of geometry
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Hines, Andrew Peter. "Entanglement, dynamical bifurcations and quantum phase transitions /." [St. Lucia, Qld.], 2005. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe19792.pdf.
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