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Journal articles on the topic 'State reconstruction, quantum tomography'

Author: Grafiati

Published: 17 September 2021

Last updated: 9 February 2022

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1

Czerwinski, Artur. "Dynamic State Reconstruction of Quantum Systems Subject to Pure Decoherence." International Journal of Theoretical Physics 59, no. 11 (October 23, 2020): 3646–61. http://dx.doi.org/10.1007/s10773-020-04625-8.

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Abstract The article introduces efficient quantum state tomography schemes for qutrits and entangled qubits subject to pure decoherence. We implement the dynamic state reconstruction method for open systems sent through phase-damping channels, which was proposed in: Czerwinski and Jamiolkowski Open Syst. Inf. Dyn. 23, 1650019 (2016). In the present article we prove that two distinct observables measured at four different time instants suffice to reconstruct the initial density matrix of a qutrit with evolution given by a phase-damping channel. Furthermore, we generalize the approach in order to determine criteria for quantum tomography of entangled qubits. Finally, we prove two universal theorems concerning the number of observables required for quantum state tomography of qudits subject to pure decoherence. We believe that dynamic state reconstruction schemes bring advancement and novelty to quantum tomography since they utilize the Heisenberg representation and allow to define the measurements in time domain.

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2

Kliesch, Martin, Richard Kueng, Jens Eisert, and David Gross. "Guaranteed recovery of quantum processes from few measurements." Quantum 3 (August 12, 2019): 171. http://dx.doi.org/10.22331/q-2019-08-12-171.

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Quantum process tomography is the task of reconstructing unknown quantum channels from measured data. In this work, we introduce compressed sensing-based methods that facilitate the reconstruction of quantum channels of low Kraus rank. Our main contribution is the analysis of a natural measurement model for this task: We assume that data is obtained by sending pure states into the channel and measuring expectation values on the output. Neither ancillary systems nor coherent operations across multiple channel uses are required. Most previous results on compressed process reconstruction reduce the problem to quantum state tomography on the channel's Choi matrix. While this ansatz yields recovery guarantees from an essentially minimal number of measurements, physical implementations of such schemes would typically involve ancillary systems. A priori, it is unclear whether a measurement model tailored directly to quantum process tomography might require more measurements. We establish that this is not the case.Technically, we prove recovery guarantees for three different reconstruction algorithms. The reconstructions are based on a trace, diamond, and ℓ2-norm minimization, respectively. Our recovery guarantees are uniform in the sense that with one random choice of measurement settings all quantum channels can be recovered equally well. Moreover, stability against arbitrary measurement noise and robustness against violations of the low-rank assumption is guaranteed. Numerical studies demonstrate the feasibility of the approach.

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3

Shahandeh, Farid, and Martin Ringbauer. "Optomechanical state reconstruction and nonclassicality verification beyond the resolved-sideband regime." Quantum 3 (February 25, 2019): 125. http://dx.doi.org/10.22331/q-2019-02-25-125.

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Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices. Yet, the challenge of reconstructing and verifying the quantum state of mechanical systems has remained a major roadblock in the field. Here, we present a novel approach that allows for tomographic reconstruction of the quantum state of a mechanical system without the need for extremely high quality optical cavities. We show that, without relying on the usual state transfer presumption between light an mechanics, the full optomechanical Hamiltonian can be exploited to imprint mechanical tomograms on a strong optical coherent pulse, which can then be read out using well-established techniques. Furthermore, with only a small number of measurements, our method can be used to witness nonclassical features of mechanical systems without requiring full tomography. By relaxing the experimental requirements, our technique thus opens a feasible route towards verifying the quantum state of mechanical resonators and their nonclassical behaviour in a wide range of optomechanical systems.

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4

REZAEE, M., M. A. JAFARIZADEH, and M. MIRZAEE. "GROUP THEORETICAL APPROACH TO QUANTUM ENTANGLEMENT AND TOMOGRAPHY WITH WAVELET TRANSFORM IN BANACH SPACES." International Journal of Quantum Information 05, no. 03 (June 2007): 367–86. http://dx.doi.org/10.1142/s0219749907002967.

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The intimate connection between the Banach space wavelet reconstruction method for each unitary representation of a given group and some of well-known quantum tomographies, such as tomography of rotation group, spinor tomography and tomography of unitary group, is established. Also both the atomic decomposition and Banach frame nature of these quantum tomographic examples are revealed in detail. Finally, we consider separability criteria for any state with group theoretical wavelet transform on Banach spaces.

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5

Zhang, Jiaojiao, Kezhi Li, Shuang Cong, and Haitao Wang. "Efficient reconstruction of density matrices for high dimensional quantum state tomography." Signal Processing 139 (October 2017): 136–42. http://dx.doi.org/10.1016/j.sigpro.2017.04.007.

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6

Chantasri, Areeya, Shengshi Pang, Teerawat Chalermpusitarak, and Andrew N. Jordan. "Quantum state tomography with time-continuous measurements: reconstruction with resource limitations." Quantum Studies: Mathematics and Foundations 7, no. 1 (May 27, 2019): 23–47. http://dx.doi.org/10.1007/s40509-019-00198-2.

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7

Ibort, Alberto, and Alberto López-Yela. "Quantum tomography and the quantum Radon transform." Inverse Problems & Imaging 15, no. 5 (2021): 893. http://dx.doi.org/10.3934/ipi.2021021.

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<p style='text-indent:20px;'>A general framework for the tomographical description of states, that includes, among other tomographical schemes, the classical Radon transform, quantum state tomography and group quantum tomography, in the setting of <inline-formula><tex-math id="M1">\begin{document}$ C^* $\end{document}</tex-math></inline-formula>-algebras is presented. Given a <inline-formula><tex-math id="M2">\begin{document}$ C^* $\end{document}</tex-math></inline-formula>-algebra, the main ingredients for a tomographical description of its states are identified: A generalized sampling theory and a positive transform. A generalization of the notion of dual tomographic pair provides the background for a sampling theory on <inline-formula><tex-math id="M3">\begin{document}$ C^* $\end{document}</tex-math></inline-formula>-algebras and, an extension of Bochner's theorem for functions of positive type, the positive transform.</p><p style='text-indent:20px;'>The abstract theory is realized by using dynamical systems, that is, groups represented on <inline-formula><tex-math id="M4">\begin{document}$ C^* $\end{document}</tex-math></inline-formula>-algebra. Using a fiducial state and the corresponding GNS construction, explicit expressions for tomograms associated with states defined by density operators on the corresponding Hilbert spade are obtained. In particular a general quantum version of the classical definition of the Radon transform is presented. The theory is completed by proving that if the representation of the group is square integrable, the representation itself defines a dual tomographic map and explicit reconstruction formulas are obtained by making a judiciously use of the theory of frames. A few significant examples are discussed that illustrates the use and scope of the theory.</p>

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8

Teo, Yong Siah, Christian R. Müller, Hyunseok Jeong, Zdeněk Hradil, Jaroslav Řeháček, and Luis L. Sánchez-Soto. "Joint measurement of complementary observables in moment tomography." International Journal of Quantum Information 15, no. 08 (December 2017): 1740002. http://dx.doi.org/10.1142/s0219749917400020.

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Wigner and Husimi quasi-distributions, owing to their functional regularity, give the two archetypal and equivalent representations of all observable-parameters in continuous-variable quantum information. Balanced homodyning (HOM) and heterodyning (HET) that correspond to their associated sampling procedures, on the other hand, fare very differently concerning their state or parameter reconstruction accuracies. We present a general theory of a now-known fact that HET can be tomographically more powerful than balanced homodyning to many interesting classes of single-mode quantum states, and discuss the treatment for two-mode sources.

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9

Czerwiński, Artur, and Andrzej Jamiołkowski. "Dynamic Quantum Tomography Model for Phase-Damping Channels." Open Systems & Information Dynamics 23, no. 04 (December 2016): 1650019. http://dx.doi.org/10.1142/s1230161216500190.

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In this paper we propose a dynamic quantum tomography model for open quantum systems with evolution given by phase-damping channels. Mathematically, these channels correspond to completely positive trace-preserving maps defined by the Hadamard product of the initial density matrix with a time-dependent matrix which carries the knowledge about the evolution. Physically, there is a strong motivation for considering this kind of evolution because such channels appear naturally in the theory of open quantum systems. The main idea behind a dynamic approach to quantum tomography claims that by performing the same kind of measurement at some time instants one can obtain new data for state reconstruction. Thus, this approach leads to a decrease in the number of distinct observables which are required for quantum tomography; however, the exact benefit for employing the dynamic approach depends strictly on how the quantum system evolves in time. Algebraic analysis of phase-damping channels allows one to determine criteria for quantum tomography of systems in question. General theorems and observations presented in the paper are accompanied by a specific example, which shows step by step how the theory works. The results introduced in this paper can potentially be applied in experiments where there is a tendency to look at quantum tomography from the point of view of economy of measurements, because each distinct kind of measurement requires, in general, preparing a separate setup.

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10

Niestegge, Gerd. "Local tomography and the role of the complex numbers in quantum mechanics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2238 (June 2020): 20200063. http://dx.doi.org/10.1098/rspa.2020.0063.

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Various reconstructions of finite-dimensional quantum mechanics result in a formally real Jordan algebra A and a last step remains to conclude that A is the self-adjoint part of a C*-algebra. Using a quantum logical setting, it is shown that this can be achieved by postulating that there is a locally tomographic model for a composite system consisting of two copies of the same system. Local tomography is a feature of classical probability theory and quantum mechanics; it means that state tomography for a multipartite system can be performed by simultaneous measurements in all subsystems. The quantum logical definition of local tomography is sufficient, but it is less restrictive than the prevalent definition in the literature and involves some subtleties concerning the so-called spin factors.

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11

Chen, Bing, Jianpei Geng, Feifei Zhou, Lingling Song, Heng Shen, and Nanyang Xu. "Quantum state tomography of a single electron spin in diamond with Wigner function reconstruction." Applied Physics Letters 114, no. 4 (January 28, 2019): 041102. http://dx.doi.org/10.1063/1.5082878.

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12

Fortunato, Mauro, Michol Massini, Stefano Mancini, and Paolo Tombesi. "Entangled State Reconstruction of an Electron in the Penning Trap." Zeitschrift für Naturforschung A 56, no. 1-2 (February 1, 2001): 145–51. http://dx.doi.org/10.1515/zna-2001-0122.

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Abstract We apply a tomographic method we have recently proposed to the reconstruction of the full entangled quantum state for the cyclotron and spin degrees of freedom of a trapped electron. Our numerical simulations show that the entangled state is accurately reconstructed. -Pacs: 03.65.

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13

Maciejewski, Filip B., Zoltán Zimborás, and Michał Oszmaniec. "Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography." Quantum 4 (April 24, 2020): 257. http://dx.doi.org/10.22331/q-2020-04-24-257.

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We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.

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14

Luchnikov, Ilia A., Alexander Ryzhov, Pieter-Jan Stas, Sergey N. Filippov, and Henni Ouerdane. "Variational Autoencoder Reconstruction of Complex Many-Body Physics." Entropy 21, no. 11 (November 7, 2019): 1091. http://dx.doi.org/10.3390/e21111091.

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Thermodynamics is a theory of principles that permits a basic description of the macroscopic properties of a rich variety of complex systems from traditional ones, such as crystalline solids, gases, liquids, and thermal machines, to more intricate systems such as living organisms and black holes to name a few. Physical quantities of interest, or equilibrium state variables, are linked together in equations of state to give information on the studied system, including phase transitions, as energy in the forms of work and heat, and/or matter are exchanged with its environment, thus generating entropy. A more accurate description requires different frameworks, namely, statistical mechanics and quantum physics to explore in depth the microscopic properties of physical systems and relate them to their macroscopic properties. These frameworks also allow to go beyond equilibrium situations. Given the notably increasing complexity of mathematical models to study realistic systems, and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models show limitations in scope or applicability. On the other hand, machine learning, i.e., data-driven, methods prove to be increasingly efficient for the study of complex quantum systems. Deep neural networks, in particular, have been successfully applied to many-body quantum dynamics simulations and to quantum matter phase characterization. In the present work, we show how to use a variational autoencoder (VAE)—a state-of-the-art tool in the field of deep learning for the simulation of probability distributions of complex systems. More precisely, we transform a quantum mechanical problem of many-body state reconstruction into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show, with the paradigmatic quantum Ising model in a transverse magnetic field, that the ground-state physics, such as, e.g., magnetization and other mean values of observables, of a whole class of quantum many-body systems can be reconstructed by using VAE learning of tomographic data for different parameters of the Hamiltonian, and even if the system undergoes a quantum phase transition. We also discuss challenges related to our approach as entropy calculations pose particular difficulties.

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15

Czartowski, Jakub, and Karol Życzkowski. "Bipartite quantum measurements with optimal single-sided distinguishability." Quantum 5 (April 26, 2021): 442. http://dx.doi.org/10.22331/q-2021-04-26-442.

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We analyse orthogonal bases in a composite N×N Hilbert space describing a bipartite quantum system and look for a basis with optimal single-sided mutual state distinguishability. This condition implies that in each subsystem the N2 reduced states form a regular simplex of a maximal edge length, defined with respect to the trace distance. In the case N=2 of a two-qubit system our solution coincides with the elegant joint measurement introduced by Gisin. We derive explicit expressions of an analogous constellation for N=3 and provide a general construction of N2 states forming such an optimal basis in HN⊗HN. Our construction is valid for all dimensions for which a symmetric informationally complete (SIC) generalized measurement is known. Furthermore, we show that the one-party measurement that distinguishes the states of an optimal basis of the composite system leads to a local quantum state tomography with a linear reconstruction formula. Finally, we test the introduced tomographical scheme on a complete set of three mutually unbiased bases for a single qubit using two different IBM machines.

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16

Richter, Th. "On tomographic reconstruction of the quantum state of a two-mode light field." Journal of Modern Optics 44, no. 11-12 (November 1997): 2385–94. http://dx.doi.org/10.1080/09500349708231889.

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17

Sentís, Gael, Johannes N. Greiner, Jiangwei Shang, Jens Siewert, and Matthias Kleinmann. "Bound entangled states fit for robust experimental verification." Quantum 2 (December 18, 2018): 113. http://dx.doi.org/10.22331/q-2018-12-18-113.

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Preparing and certifying bound entangled states in the laboratory is an intrinsically hard task, due to both the fact that they typically form narrow regions in state space, and that a certificate requires a tomographic reconstruction of the density matrix. Indeed, the previous experiments that have reported the preparation of a bound entangled state relied on such tomographic reconstruction techniques. However, the reliability of these results crucially depends on the extra assumption of an unbiased reconstruction. We propose an alternative method for certifying the bound entangled character of a quantum state that leads to a rigorous claim within a desired statistical significance, while bypassing a full reconstruction of the state. The method is comprised by a search for bound entangled states that are robust for experimental verification, and a hypothesis test tailored for the detection of bound entanglement that is naturally equipped with a measure of statistical significance. We apply our method to families of states of3×3and4×4systems, and find that the experimental certification of bound entangled states is well within reach.

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18

Pezzè, Luca, Yan Li, Weidong Li, and Augusto Smerzi. "Witnessing entanglement without entanglement witness operators." Proceedings of the National Academy of Sciences 113, no. 41 (September 28, 2016): 11459–64. http://dx.doi.org/10.1073/pnas.1603346113.

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Quantum mechanics predicts the existence of correlations between composite systems that, although puzzling to our physical intuition, enable technologies not accessible in a classical world. Notwithstanding, there is still no efficient general method to theoretically quantify and experimentally detect entanglement of many qubits. Here we propose to detect entanglement by measuring the statistical response of a quantum system to an arbitrary nonlocal parametric evolution. We witness entanglement without relying on the tomographic reconstruction of the quantum state, or the realization of witness operators. The protocol requires two collective settings for any number of parties and is robust against noise and decoherence occurring after the implementation of the parametric transformation. To illustrate its user friendliness we demonstrate multipartite entanglement in different experiments with ions and photons by analyzing published data on fidelity visibilities and variances of collective observables.

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19

Adesso, Gerardo, Alessio Serafini, and Fabrizio Illuminati. "Entanglement, Purity, and Information Entropies in Continuous Variable Systems." Open Systems & Information Dynamics 12, no. 02 (June 2005): 189–205. http://dx.doi.org/10.1007/s11080-005-5730-2.

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Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal (i.e. referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or, in general, by information entropies, provides an accurate characterization of its entanglement. In particular, for Gaussian states of continuous variable systems, we classify the entanglement of two-mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized p-entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entanglement in highly symmetric Gaussian states of arbitrary 1 × N-mode partitions.

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20

Teo, Yong Siah, Hyunseok Jeong, Jaroslav Řeháček, Zdeněk Hradil, Luis L. Sánchez-Soto, and Christine Silberhorn. "On the Prospects of Multiport Devices for Photon-Number-Resolving Detection." Quantum Reports 1, no. 2 (September 29, 2019): 162–80. http://dx.doi.org/10.3390/quantum1020015.

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Ideal photon-number-resolving detectors form a class of important optical components in quantum optics and quantum information theory. In this article, we theoretically investigate the potential of multiport devices having reconstruction performances approaching that of the Fock-state measurement. By recognizing that all multiport devices are minimally complete, we first provide a general analytical framework to describe the tomographic accuracy (or quality) of these devices. Next, we show that a perfect multiport device with an infinite number of output ports functions as either the Fock-state measurement when photon losses are absent or binomial mixtures of Fock-state measurements when photon losses are present and derive their respective expressions for the tomographic transfer function. This function is the scaled asymptotic mean squared error of the reconstructed photon-number distributions uniformly averaged over all distributions in the probability simplex. We then supply more general analytical formulas for the transfer function for finite numbers of output ports in both the absence and presence of photon losses. The effects of photon losses on the photon-number resolving power of both infinite- and finite-size multiport devices are also investigated.

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21

KONG, LINGCHEN, and NAIHUA XIU. "EXACT LOW-RANK MATRIX RECOVERY VIA NONCONVEX SCHATTEN p-MINIMIZATION." Asia-Pacific Journal of Operational Research 30, no. 03 (June 2013): 1340010. http://dx.doi.org/10.1142/s0217595913400101.

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The low-rank matrix recovery (LMR) arises in many fields such as signal and image processing, quantum state tomography, magnetic resonance imaging, system identification and control, and it is generally NP-hard. Recently, Majumdar and Ward [Majumdar, A and RK Ward (2011). An algorithm for sparse MRI reconstruction by Schatten p-norm minimization. Magnetic Resonance Imaging, 29, 408–417]. had successfully applied nonconvex Schatten p-minimization relaxation of LMR in magnetic resonance imaging. In this paper, our main aim is to establish RIP theoretical result for exact LMR via nonconvex Schatten p-minimization. Carefully speaking, letting [Formula: see text] be a linear transformation from ℝm×n into ℝs and r be the rank of recovered matrix X ∈ ℝm×n, and if [Formula: see text] satisfies the RIP condition [Formula: see text] for a given positive integer k ∈ {1, 2, …, m – r}, then r-rank matrix can be exactly recovered. In particular, we obtain a uniform bound on restricted isometry constant [Formula: see text] for any p ∈ (0, 1] for LMR via Schatten p-minimization.

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22

Nawaz, Ahmad. "Quantum State Tomography and Quantum Games." Chinese Physics Letters 29, no. 3 (March 2012): 030308. http://dx.doi.org/10.1088/0256-307x/29/3/030308.

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23

Johansen, Lars M. "Hydrodynamical Quantum State Reconstruction." Physical Review Letters 80, no. 25 (June 22, 1998): 5461–64. http://dx.doi.org/10.1103/physrevlett.80.5461.

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24

Ramadhani, Syahri, Junaid Ur Rehman, and Hyundong Shin. "Quantum Error Mitigation for Quantum State Tomography." IEEE Access 9 (2021): 107955–64. http://dx.doi.org/10.1109/access.2021.3101214.

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25

Torlai, Giacomo, Guglielmo Mazzola, Juan Carrasquilla, Matthias Troyer, Roger Melko, and Giuseppe Carleo. "Neural-network quantum state tomography." Nature Physics 14, no. 5 (February 26, 2018): 447–50. http://dx.doi.org/10.1038/s41567-018-0048-5.

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26

Brańczyk, A. M., D. H. Mahler, L. A. Rozema, A. Darabi, A. M. Steinberg, and D. F. V. James. "Self-calibrating quantum state tomography." New Journal of Physics 14, no. 8 (August 1, 2012): 085003. http://dx.doi.org/10.1088/1367-2630/14/8/085003.

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27

Mouritzen, Anders S., and Klaus Mølmer. "Quantum state tomography of molecular rotation." Journal of Chemical Physics 124, no. 24 (June 28, 2006): 244311. http://dx.doi.org/10.1063/1.2208351.

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Lvovsky, A. I., and M. G. Raymer. "Continuous-variable optical quantum-state tomography." Reviews of Modern Physics 81, no. 1 (March 16, 2009): 299–332. http://dx.doi.org/10.1103/revmodphys.81.299.

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29

D'Ariano, G. M., M. Rubin, M. F. Sacchi, and Y. Shih. "Quantum Tomography of the GHZ State." Fortschritte der Physik 48, no. 5-7 (May 2000): 599–603. http://dx.doi.org/10.1002/(sici)1521-3978(200005)48:5/7<599::aid-prop599>3.0.co;2-h.

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Liu, Yu-xi, L. F. Wei, and Franco Nori. "Quantum tomography for solid-state qubits." Europhysics Letters (EPL) 67, no. 6 (September 2004): 874–80. http://dx.doi.org/10.1209/epl/i2004-10154-1.

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31

Beck, M. "Quantum State Tomography with Array Detectors." Physical Review Letters 84, no. 25 (June 19, 2000): 5748–51. http://dx.doi.org/10.1103/physrevlett.84.5748.

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32

Kalev, Amir, and Pier A. Mello. "Quantum state tomography using successive measurements." Journal of Physics A: Mathematical and Theoretical 45, no. 23 (May 18, 2012): 235301. http://dx.doi.org/10.1088/1751-8113/45/23/235301.

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33

Gonçalves, D. S., C. L. N. Azevedo, C. Lavor, and M. A. Gomes-Ruggiero. "Bayesian inference for quantum state tomography." Journal of Applied Statistics 45, no. 10 (November 15, 2017): 1846–71. http://dx.doi.org/10.1080/02664763.2017.1401049.

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34

Huang, Huikang, Haozhen Situ, and Shenggen Zheng. "Bidirectional Information Flow Quantum State Tomography." Chinese Physics Letters 38, no. 4 (May 1, 2021): 040303. http://dx.doi.org/10.1088/0256-307x/38/4/040303.

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35

Lvovsky, A. I. "Iterative maximum-likelihood reconstruction in quantum homodyne tomography." Journal of Optics B: Quantum and Semiclassical Optics 6, no. 6 (May 29, 2004): S556—S559. http://dx.doi.org/10.1088/1464-4266/6/6/014.

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36

Deshpande, Sarin A., and Gregory S. Ezra. "Quantum state reconstruction for rigid rotors." Chemical Physics Letters 440, no. 4-6 (June 2007): 341–47. http://dx.doi.org/10.1016/j.cplett.2007.04.049.

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37

Khanna, F. C., P. A. Mello, and M. Revzen. "Classical and quantum-mechanical state reconstruction." European Journal of Physics 33, no. 4 (May 14, 2012): 921–39. http://dx.doi.org/10.1088/0143-0807/33/4/921.

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38

Lovecchio, C., S. Cherukattil, B. Cilenti, I. Herrera, F. S. Cataliotti, S. Montangero, T. Calarco, and F. Caruso. "Quantum state reconstruction on atom-chips." New Journal of Physics 17, no. 9 (September 16, 2015): 093024. http://dx.doi.org/10.1088/1367-2630/17/9/093024.

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39

Ghiglieri, J., and M. G. A. Paris. "Quantum state reconstruction by entangled measurements." European Physical Journal D 40, no. 1 (June 15, 2006): 139–46. http://dx.doi.org/10.1140/epjd/e2006-00129-8.

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40

Collins, Graham P. "Quantum State Reconstruction of Squeezed Light." Physics Today 50, no. 8 (August 1997): 18. http://dx.doi.org/10.1063/1.881854.

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41

Wu, Lian-Ao, and Mark S. Byrd. "Self-protected quantum algorithms based on quantum state tomography." Quantum Information Processing 8, no. 1 (December 16, 2008): 1–12. http://dx.doi.org/10.1007/s11128-008-0090-9.

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42

Leonhardt, Ulf. "Discrete Wigner function and quantum-state tomography." Physical Review A 53, no. 5 (May 1, 1996): 2998–3013. http://dx.doi.org/10.1103/physreva.53.2998.

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43

Miroshnichenko, G. P., and O. M. Korneeva. "Quantum state tomography of the microwave field." Journal of Physics: Conference Series 541 (October 27, 2014): 012101. http://dx.doi.org/10.1088/1742-6596/541/1/012101.

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44

YAMAGATA, KOICHI. "EFFICIENCY OF QUANTUM STATE TOMOGRAPHY FOR QUBITS." International Journal of Quantum Information 09, no. 04 (June 2011): 1167–83. http://dx.doi.org/10.1142/s0219749911007551.

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Abstract:

The efficiency of quantum state tomography is discussed from the point of view of quantum parameter estimation theory, in which the trace of the weighted covariance is to be minimized. It is shown that tomography is optimal only when a special weight is adopted.

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45

Fujiwara, Akio, and Koichi Yamagata. "Information Geometry of Randomized Quantum State Tomography." Entropy 20, no. 8 (August 16, 2018): 609. http://dx.doi.org/10.3390/e20080609.

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Suppose that a d-dimensional Hilbert space H ≃ C d admits a full set of mutually unbiased bases | 1 ( a ) 〉 , ⋯ , | d ( a ) 〉 , where a = 1 , ⋯ , d + 1 . A randomized quantum state tomography is a scheme for estimating an unknown quantum state on H through iterative applications of measurements M ( a ) = | 1 ( a ) 〉 〈 1 ( a ) | , ⋯ , | d ( a ) 〉 〈 d ( a ) | for a = 1 , ⋯ , d + 1 , where the numbers of applications of these measurements are random variables. We show that the space of the resulting probability distributions enjoys a mutually orthogonal dualistic foliation structure, which provides us with a simple geometrical insight into the maximum likelihood method for the quantum state tomography.

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46

Scerri, Dale, Erik M. Gauger, and George C. Knee. "Coarse-graining in retrodictive quantum state tomography." Journal of Physics Communications 3, no. 7 (July 8, 2019): 075003. http://dx.doi.org/10.1088/2399-6528/ab0aa9.

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47

Dominguez, D., C. J. Regan, A. A. Bernussi, and L. Grave de Peralta. "Toward surface plasmon polariton quantum-state tomography." Journal of Applied Physics 113, no. 7 (February 21, 2013): 073102. http://dx.doi.org/10.1063/1.4792305.

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48

Leonhardt, Ulf. "Quantum-State Tomography and Discrete Wigner Function." Physical Review Letters 74, no. 21 (May 22, 1995): 4101–5. http://dx.doi.org/10.1103/physrevlett.74.4101.

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49

Leonhardt, Ulf. "Quantum-State Tomography and Discrete Wigner Function." Physical Review Letters 76, no. 22 (May 27, 1996): 4293. http://dx.doi.org/10.1103/physrevlett.76.4293.

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50

Anis, Aamir, and A. I. Lvovsky. "Maximum-likelihood coherent-state quantum process tomography." New Journal of Physics 14, no. 10 (October 19, 2012): 105021. http://dx.doi.org/10.1088/1367-2630/14/10/105021.

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