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Journal articles on the topic 'Absolutely Maximally Entangled states'

Author: Grafiati

Published: 24 April 2022

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1

Mansour, M., M. Daoud, and L. Bouhouch. "Absolutely maximally entangled states from phase states." International Journal of Quantum Information 17, no. 01 (2019): 1950009. http://dx.doi.org/10.1142/s0219749919500096.

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We derive absolutely maximally entangled (AME) states from phase states for a multi-qudit system whose dynamics is governed by a two-qudit interaction Hamiltonian of Heisenberg type. AME states are characterized by being maximally entangled for all bipartitions of the multi-qudit system and present absolute multipartite entanglement. The key ingredient of this approach is the theory of phase states for finite-dimensional systems (qudits). We define further the unitary phase operators of [Formula: see text]-qudit systems and we give next the corresponding separable phase states. Using a qudit–q

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2

Raissi, Zahra, Christian Gogolin, Arnau Riera, and Antonio Acín. "Optimal quantum error correcting codes from absolutely maximally entangled states." Journal of Physics A: Mathematical and Theoretical 51, no. 7 (2018): 075301. http://dx.doi.org/10.1088/1751-8121/aaa151.

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3

Bernal, Antonio. "On the Existence of Absolutely Maximally Entangled States of Minimal Support II." Quantum Physics Letters 8, no. 1 (2019): 1–4. http://dx.doi.org/10.18576/qpl/080101.

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4

Huber, Felix, Christopher Eltschka, Jens Siewert, and Otfried Gühne. "Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity." Journal of Physics A: Mathematical and Theoretical 51, no. 17 (2018): 175301. http://dx.doi.org/10.1088/1751-8121/aaade5.

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5

Huber, Felix, and Markus Grassl. "Quantum Codes of Maximal Distance and Highly Entangled Subspaces." Quantum 4 (June 18, 2020): 284. http://dx.doi.org/10.22331/q-2020-06-18-284.

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We present new bounds on the existence of general quantum maximum distance separable codes (QMDS): the length n of all QMDS codes with local dimension D and distance d≥3 is bounded by n≤D2+d−2. We obtain their weight distribution and present additional bounds that arise from Rains' shadow inequalities. Our main result can be seen as a generalization of bounds that are known for the two special cases of stabilizer QMDS codes and absolutely maximally entangled states, and confirms the quantum MDS conjecture in the special case of distance-three codes. As the existence of QMDS codes is linked to

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6

Reuvers, R. "An algorithm to explore entanglement in small systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2214 (2018): 20180023. http://dx.doi.org/10.1098/rspa.2018.0023.

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A quantum state’s entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms. Depending on the choice of norm, the optimizing states maximize or minimize entanglement, possibly across several bipartite cuts at the same time and possibly only among states in a specified subspace. Recognizing that convergence but not success is certain, we use the algorithm to explore topics ranging from fermionic reduced density matrices and varieties of pu

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7

I. Latorre, Jose, and German Sierra. "Platonic entanglement." Quantum Information and Computation 21, no. 13&14 (2021): 1081–90. http://dx.doi.org/10.26421/qic21.13-14-1.

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We present a construction of highly entangled states defined on the topology of a platonic solid using tensor networks based on ancillary Absolute Maximally Entangled (AME) states. We illustrate the idea using the example of a quantum state based on AME(5,2) over a dodecahedron. We analyze the entropy of such states on many different partitions, and observe that they come on integer numbers and are almost maximal. We also observe that all platonic solids accept the construction of AME states based on Reed-Solomon codes since their number of facets, vertices and edges are always a prime number

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8

Bernal, Antonio. "On the Existence of Absolutely Maximally Entangled States of Minimal Support Physical Consistency of Theories with Fermions in the Division Algebra Modules." Quantum Physics Letters 6, no. 1 (2017): 1–3. http://dx.doi.org/10.18576/qpl/060101.

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9

Revzen, M. "Universal maximally entangled states." Quantum Studies: Mathematics and Foundations 2, no. 1 (2014): 77–88. http://dx.doi.org/10.1007/s40509-014-0016-4.

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10

Li, Z. G., M. G. Zhao, S. M. Fei, H. Fan, and W. M. Liu. "Mixed maximally entangled states." Quantum Information and Computation 12, no. 1&2 (2012): 63–73. http://dx.doi.org/10.26421/qic12.1-2-5.

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We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other entanglement measures, this conclusion is still proven right. This result is a supplementary to the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states, for example, these states can be used as a resource for faithful teleportation and they can be distinguished perfectl

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11

Adhikari, S., A. S. Majumdar, S. Roy, B. Ghosh, and N. Nayak. "Teleportation via maximally and non-maximally entangled mixed states." Quantum Information and Computation 10, no. 5&6 (2010): 398–419. http://dx.doi.org/10.26421/qic10.5-6-3.

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We study the efficiency of two-qubit mixed entangled states as resources for quantum teleportation. We first consider two maximally entangled mixed states, viz., the Werner state\cite{werner}, and a class of states introduced by Munro {\it et al.} \cite{munro}. We show that the Werner state when used as teleportation channel, gives rise to better average teleportation fidelity compared to the latter class of states for any finite value of mixedness. We then introduce a non-maximally entangled mixed state obtained as a convex combination of a two-qubit entangled mixed state and a two-qubit sepa

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12

Poon, Edward. "Preservers of maximally entangled states." Linear Algebra and its Applications 468 (March 2015): 122–44. http://dx.doi.org/10.1016/j.laa.2014.03.009.

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13

Agrawal, Pankaj, and B. Pradhan. "Task-oriented maximally entangled states." Journal of Physics A: Mathematical and Theoretical 43, no. 23 (2010): 235302. http://dx.doi.org/10.1088/1751-8113/43/23/235302.

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14

Mansour, Mostafa, and Saeed Haddadi. "Bipartite entanglement of decohered mixed states generated from maximally entangled cluster states." Modern Physics Letters A 36, no. 03 (2021): 2150010. http://dx.doi.org/10.1142/s0217732321500103.

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In this work, we investigate the bipartite entanglement of decohered mixed states generated from maximally entangled cluster states of [Formula: see text] qubits physical system. We introduce the disconnected cluster states for an ensemble of [Formula: see text] non-interacting qubits and we give the corresponding separable density matrices. The maximally entangled states can be generated from disconnected cluster states, by assuming that the dynamics of the multi-qubit system is governed by a quadratic Hamiltonian of Ising type. When exposed to a local noisy interaction with the environment,

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15

Varma, Anant Vijay, Anvesh Raja Kovela, Prasanta K. Panigrahi, and Bhavesh Chouhan. "Entanglement and quantum phase transition in topological insulators." Modern Physics Letters B 33, no. 32 (2019): 1950394. http://dx.doi.org/10.1142/s0217984919503949.

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Presence of entangled states is explicitly shown in a topological insulator (TI) [Formula: see text]. The surface and bulk state are found to have different structures of entanglement. The surface states live as maximally entangled states in a four-dimensional subspace of total Hilbert space (spin, orbital, space). However, bulk states are entangled in the whole Hilbert space. Bulk states are found to be entangled maximally by controlled injection of electrons with momentum only along the [Formula: see text]-direction. At quantum phase transition (QPT) point, both states become maximally entan

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16

Gour, Gilad, and Nolan R. Wallach. "All maximally entangled four-qubit states." Journal of Mathematical Physics 51, no. 11 (2010): 112201. http://dx.doi.org/10.1063/1.3511477.

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17

Flores, M. M., and E. A. Galapon. "Mixtures of maximally entangled pure states." Annals of Physics 372 (September 2016): 297–308. http://dx.doi.org/10.1016/j.aop.2016.05.018.

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18

Zha, Xin-wei, Irfan Ahmed, and Yanpeng Zhang. "Constructing five qutrit absolutely maximally entangled state via recurrence relation." Laser Physics 30, no. 7 (2020): 075201. http://dx.doi.org/10.1088/1555-6611/ab8d2f.

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19

Huang, Haiqing, Irfan Ahmed, Da Zhang, Xin-wei Zha, and Yanpeng Zhang. "Constructing seven ququarts absolutely maximally entangled state via recurrence relation." Laser Physics 31, no. 1 (2020): 015201. http://dx.doi.org/10.1088/1555-6611/abcf24.

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20

Obada, A. S. F., M. M. A. Ahmed, Hoda A. Ali, Somia Abd-Elnabi, and S. Sanad. "Maximally Entangled SU(1,1) Semi Coherent States." International Journal of Theoretical Physics 60, no. 4 (2021): 1425–37. http://dx.doi.org/10.1007/s10773-021-04768-2.

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AbstractIn this paper, we consider a special type of maximally entangled states namely by entangled SU(1,1) semi coherent states by using SU(1,1) semi coherent states(SU(1,1) Semi CS). The entanglement characteristics of these entangled states are studied by evaluating the concurrence.We investigate some of their nonclassical properties,especially probability distribution function,second-order correlation function and quadrature squeezing . Further, the quasiprobability distribution functions (Q-functions) is discussed.

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21

Grossmann, Ben W., and Hugo J. Woerdeman. "On the preservers of maximally entangled states." Linear Algebra and its Applications 583 (December 2019): 171–94. http://dx.doi.org/10.1016/j.laa.2019.09.004.

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22

Enríquez, M., I. Wintrowicz, and K. Życzkowski. "Maximally Entangled Multipartite States: A Brief Survey." Journal of Physics: Conference Series 698 (March 2016): 012003. http://dx.doi.org/10.1088/1742-6596/698/1/012003.

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23

Chung, Ming-Chiang, Yi-Hao Jhu, Pochung Chen, and Chung-Yu Mou. "Quench dynamics of topological maximally entangled states." Journal of Physics: Condensed Matter 25, no. 28 (2013): 285601. http://dx.doi.org/10.1088/0953-8984/25/28/285601.

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24

Feng, Tian, Zhihua Guo, and Huaixin Cao. "Witness for Non-Quasi Maximally Entangled States." International Journal of Theoretical Physics 55, no. 12 (2016): 5202–15. http://dx.doi.org/10.1007/s10773-016-3141-5.

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25

Cereceda, JoséL. "Maximally entangled states and the Bell inequality." Physics Letters A 212, no. 3 (1996): 123–29. http://dx.doi.org/10.1016/0375-9601(96)00026-6.

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26

Kaur, Hargeet, and Atul Kumar. "An Improved Ping-Pong Protocol Using Three-Qubit Nonmaximally Nonorthogonal Entangled States." Zeitschrift für Naturforschung A 74, no. 9 (2019): 799–811. http://dx.doi.org/10.1515/zna-2018-0448.

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AbstractWe analyse the ping-pong (PP) protocol [K. Bostrom and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002)] using different sets of partially entangled three-qubit states. Interestingly, our results show that the partially entangled nonorthogonal three-qubit states are more useful as resources in comparison to three-qubit maximally entangled Greenberger–Horne–Zeilinger (GHZ) states. The properties of orthogonal set of partially entangled states as resources for PP protocol, however, are similar to that of maximally entangled GHZ states – both the states are not preferable due to the vulne

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27

Keyl, M., D. Schlingemann, and R. F. Werner. "Infinitely entangled states." Quantum Information and Computation 3, no. 4 (2003): 281–306. http://dx.doi.org/10.26421/qic3.4-1.

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For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as a resource for tasks like the teleportation of arbitrarily many qubits. We show that appropriate states cannot be obtained by density operators in an infinite dimensional Hilbert space. However, using techniques for the description of infinitely many degrees of freedom from field theory and statistical mechanics, such states can nevertheless be constructed

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28

Wang, Chenghong, Kun Wang та Zhu-Jun Zheng. "Construction of a Family of Maximally Entangled Bases in ℂd ⊗ ℂd′". Entropy 24, № 3 (2022): 373. http://dx.doi.org/10.3390/e24030373.

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In this paper, we present a new method for the construction of maximally entangled states in Cd⊗Cd′ when d′≥2d. A systematic way of constructing a set of maximally entangled bases (MEBs) in Cd⊗Cd′ was established. Both cases when d′ is divisible by d and not divisible by d are discussed. We give two examples of maximally entangled bases in C2⊗C4, which are mutually unbiased bases. Finally, we found a new example of an unextendible maximally entangled basis (UMEB) in C2⊗C5.

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29

Faujdar, Jyoti, and Atul Kumar. "Analysing the Efficiencies of Partially Entangled Three-Qubit States for Quantum Information Processing Under Real Conditions." Zeitschrift für Naturforschung A 74, no. 6 (2019): 523–37. http://dx.doi.org/10.1515/zna-2018-0521.

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AbstractIn this article, we revisit the question of analysing the efficiencies of partially entangled states in three-qubit classes under real conditions. Our results show some interesting observations regarding the efficiencies and correlations of partially entangled states. Surprisingly, we find that the efficiencies of many three-qubit partially entangled states exceed that of maximally entangled three-qubit states under real noisy conditions and applications of weak measurements. Our analysis, therefore, suggests that the efficiencies of partially entangled states are much more robust to n

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30

Chattopadhyay, I., and D. Sarkar. "Deterministic Local Conversion of Incomparable States by Collective LOCC." Quantum Information and Computation 5, no. 3 (2005): 247–57. http://dx.doi.org/10.26421/qic5.3-5.

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Incomparability of pure bipartite entangled states under deterministic LOCC is a very strange phenomena. We find two possible ways of getting our desired pure entangled state which is incomparable with the given input state, by collective LOCC with certainty. The first one is by providing some pure entanglement through the lower dimensional maximally-entangled states or using further less amount of entanglement and the next one is by collective operation on two pairs which are individually incomparable. It is quite surprising that we are able to achieve maximally entangled states of any Schmid

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31

Li, De-chao, and Zhong-ke Shi. "Probabilistic Telecloning with Partially Entangled States." Open Systems & Information Dynamics 16, no. 04 (2009): 413–22. http://dx.doi.org/10.1142/s123016120900030x.

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We propose a scheme for probabilistic telecloning of unknown d-dimensional quantum state with non-maximally (partially) entanglement via Bell measurement. The scheme requires less entanglement between the two sides, representing a much more efficient use of entanglement than the approach where Alice first clones these states on her particle and then teleports.

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32

Napoli, A., and A. Messina. "Maximally entangled states of a bimodal cavity field." Journal of Modern Optics 47, no. 12 (2000): 2105–11. http://dx.doi.org/10.1080/09500340008235133.

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33

Messina, A. Napoli, A. "Maximally entangled states of a bimodal cavity field." Journal of Modern Optics 47, no. 12 (2000): 2105–11. http://dx.doi.org/10.1080/095003400419960.

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34

Munro, W. J., and K. Nemoto. "Maximally Entangled Mixed States and the Bell Inequality." Zeitschrift für Naturforschung A 56, no. 1-2 (2001): 152–54. http://dx.doi.org/10.1515/zna-2001-0123.

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AbstractRecently a class of maximally entangled states has been proposed that has the maximum amount of entanglement for a given purity. We investigate how much such states violate the conventional Bell inequality and discuss its implication.

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35

Spee, C., J. I. de Vicente, and B. Kraus. "The maximally entangled set of 4-qubit states." Journal of Mathematical Physics 57, no. 5 (2016): 052201. http://dx.doi.org/10.1063/1.4946895.

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36

Bryan, Jim, Samuel Leutheusser, Zinovy Reichstein, and Mark Van Raamsdonk. "Locally Maximally Entangled States of Multipart Quantum Systems." Quantum 3 (January 6, 2019): 115. http://dx.doi.org/10.22331/q-2019-01-06-115.

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For a multipart quantum system, a locally maximally entangled (LME) state is one where each elementary subsystem is maximally entangled with its complement. This paper is a sequel to~[J. Bryan, Z. Reichstein and M. Van Raamsdonk, Existence of Locally Maximally Entangled Quantum States via Geometric Invariant Theory, Ann. Henri Poincaré 19 (2018), no. 8, 2491-2511. MR3830220], which gives necessary and sufficient conditions for a system to admit LME states in terms of its subsystem dimensions(d1,d2,…,dn), and computes the dimension of the spaceSLME/Kof LME states up to local unitary transformat

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37

Friedland, Shmuel, and Todd Kemp. "Most boson quantum states are almost maximally entangled." Proceedings of the American Mathematical Society 146, no. 12 (2018): 5035–49. http://dx.doi.org/10.1090/proc/13933.

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38

Dao-Hua, Zhang, Zhou Duan-Lu, and Fan Heng. "Entanglement of Superpositions of Orthogonal Maximally Entangled States." Chinese Physics Letters 27, no. 9 (2010): 090306. http://dx.doi.org/10.1088/0256-307x/27/9/090306.

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39

Singh, Manu P., and B. S. Rajput. "Maximally Entangled States of a Two-Qubit System." International Journal of Theoretical Physics 52, no. 12 (2013): 4237–55. http://dx.doi.org/10.1007/s10773-013-1736-7.

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40

Zhang, Zhi-Chao, Qiao-Yan Wen, Fei Gao, Guo-Jing Tian, and Tian-Qing Cao. "One-way LOCC indistinguishability of maximally entangled states." Quantum Information Processing 13, no. 3 (2013): 795–804. http://dx.doi.org/10.1007/s11128-013-0691-9.

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41

Duan, Junjun, Lin Zhang, Quan Qian, and Shao-Ming Fei. "A Characterization of Maximally Entangled Two-Qubit States." Entropy 24, no. 2 (2022): 247. http://dx.doi.org/10.3390/e24020247.

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As already known by Rana’s result, all eigenvalues of any partial-transposed bipartite state fall within the closed interval [−12,1]. In this note, we study a family of bipartite quantum states where the minimal eigenvalues of partial-transposed states are −12. For a two-qubit system, we find that the minimal eigenvalue of its partial-transposed state is −12 if and only if such a two-qubit state is maximally entangled. However this result does not hold in general for a two-qudit system when the dimensions of the underlying space are larger than two.

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42

Laba, H. P., and V. M. Tkachuk. "Entangled states in supersymmetric quantum mechanics." Modern Physics Letters A 35, no. 34 (2020): 2050282. http://dx.doi.org/10.1142/s021773232050282x.

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We study entanglement of spin degrees of freedom with continuous one in supersymmetric (SUSY) quantum mechanics. Concurrence is determined by mean value of spin and is calculated explicitly for SUSY states. We show that eigenstates of supercharges are maximally entangled. As an example the entanglement of atom state with photon state and SUSY in Jaynes–Cummings model are considered.

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43

Zhang, Zhanjun, Li Deng, Lei Zhang, Bin Zhuge, and Biaoliang Ye. "Efficient Tripartite Quantum Operation Sharing with Five-Qubit Absolutely Maximally Entangled State." International Journal of Theoretical Physics 60, no. 7 (2021): 2583–91. http://dx.doi.org/10.1007/s10773-020-04684-x.

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44

Methot, A. A., and V. Scarani. "An anomaly of non-locality." Quantum Information and Computation 7, no. 1&2 (2007): 157–70. http://dx.doi.org/10.26421/qic7.1-2-10.

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Ever since the work of Bell, it has been known that entangled quantum states can produce non-local correlations between the outcomes of separate measurements. However, for almost forty years, it has been assumed that the most non-local states would be the maximally entangled ones. Surprisingly it is not the case: non-maximally entangled states are generally more non-local than maximally entangled states for all the measures of non-locality proposed to date: Bell inequalities, the Kullback-Leibler distance, entanglement simulation with communication or with non-local boxes, the detection loopho

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45

Sousa, Emilio H. S., and J. A. Roversi. "Selective Engineering for Preparing Entangled Steady States in Cavity QED Setup." Quantum Reports 1, no. 1 (2019): 63–70. http://dx.doi.org/10.3390/quantum1010007.

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We propose a dissipative scheme to prepare maximally entangled steady states in cavity QED setup, consisting of two two-level atoms interacting with the two counter-propagating whispering-gallery modes (WGMs) of a microtoroidal resonator. Using spontaneous emission and cavity decay as the dissipative quantum dynamical source, we show that the steady state of this system can be steered into a two-atom single state as well as into a two-mode single state. We probed the compound system with weak field coupled to the system via a tapered fiber waveguide, finding it is possible to determine whether

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46

REZNIK, B. "REMOTE GENERALIZED MEASUREMENTS USING PARTIALLY ENTANGLED STATES." International Journal of Quantum Information 04, no. 01 (2006): 181–87. http://dx.doi.org/10.1142/s0219749906001682.

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We propose a method for implementing remotely a generalized measurement (POVM). We show that remote generalized measurements consume less entanglement compared with remote projective measurements, and can be optimally performed using non-maximally entangled states. We derive the entanglement cost of such measurements.

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47

Lockhart, R. B., M. J. Steiner, and K. Gerlach. "Geometry and product states." Quantum Information and Computation 2, no. 5 (2002): 333–47. http://dx.doi.org/10.26421/qic2.5-1.

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As separable states are a convex combination of product states, the geometry of the manifold of product states, $\Sigma$, is studied. Prior results by Sanpera, Vidal and Tarrach are extended. Furthermore, it is proven that states in the set tangent to $\Sigma$ at the maximally mixed state are separable; the set normal contains, among others, all extended GHZ states. A canonical decomposition is given. A surprising result is that for the case of two particles, the closest product state to the maximally entangled state is the maximally mixed state. An algorithm is provided to find the closest pr

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48

Zhang, Yan-Jie, Cai-Peng Shen, Zhi-Feng Pan, et al. "Concentration of entanglement in collective-rotating decoherence-free subspace." Modern Physics Letters B 34, no. 05 (2020): 2050067. http://dx.doi.org/10.1142/s0217984920500670.

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An entanglement concentration protocol in photonic collective-rotating decoherence-free subspace (CRDFS) is proposed. To accomplish the scheme, two methods to construct parity measurement devices in CRDFS are presented by exploiting the cross-Kerr nonlinearity, through which partially entangled states are converted to maximally entangled states. The performance of the protocol can be improved by iteration method. Fidelity in consideration of dissipation is discussed, which demonstrates good robustness. In contrast to the conventional protocols, the present one has distinctive feature since it

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49

Xiong, K. W. "Teleportation of unknown atomic entangled states via Greenberger–Horne–Zeilinger class states." Canadian Journal of Physics 86, no. 6 (2008): 849–51. http://dx.doi.org/10.1139/p07-204.

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A physical scheme for teleporting unknown atomic entangled states via three-atom non-maximally entangled states is proposed in cavity quantum electrodynamics. In this scheme, the Greenberger–Horne–Zeilinger class states are used as quantum channels. The most distinct feature of our scheme is that, not only the effects of the cavity decay and thermal field are eliminated, but also the teleportation and distillation procedure can be realized simultaneously.PACS Nos.: 03.67.Hk, 03.67.Pp

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50

Mansour, Mostafa, and Mohammed Daoud. "k-uniform maximally mixed states from multi-qudit phase states." Modern Physics Letters A 34, no. 19 (2019): 1950151. http://dx.doi.org/10.1142/s0217732319501517.

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This paper concerns the construction of k-uniform maximally mixed multipartite states by using the formalism of phase states for finite dimensional systems (qudits). The k-uniform states are a special kind of entangled (n)-qudits states, such that after tracing out arbitrary (n[Formula: see text]k) subsystems, the remaining (k) subsystems are maximally mixed. We recall some basic elements about unitary phase operators of a multi-qudit system and we give the corresponding separable density matrices. Evolved density matrices arise when qudits of the multipartite system are allowed to interact vi

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