Статті в журналах: "Entanglement monogamy"

1

Seevinck, M. P. "Monogamy of correlations versus monogamy of entanglement." Quantum Information Processing 9, no. 2 (January 16, 2010): 273–94. http://dx.doi.org/10.1007/s11128-009-0161-6.

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2

CHEN, LIN, and MASAHITO HAYASHI. "NONDISTILLABLE ENTANGLEMENT GUARANTEES DISTILLABLE ENTANGLEMENT." International Journal of Modern Physics B 26, no. 27n28 (September 18, 2012): 1243008. http://dx.doi.org/10.1142/s0217979212430084.

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The monogamy of entanglement is one of the basic quantum mechanical features, which says that when two partners Alice and Bob are more entangled then either of them has to be less entangled with the third party. Here we qualitatively present the converse monogamy of entanglement: given a tripartite pure system and when Alice and Bob are entangled and nondistillable, then either of them is distillable with the third party. Our result leads to the classification of tripartite pure states based on bipartite reduced density operators, which is a novel and effective way to this long-standing problem compared to the means by stochastic local operations and classical communications. Furthermore we systematically indicate the structure of the classified states and generate them. We also extend our results to multipartite states.

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3

Zhang, Meiming, and Naihuan Jing. "Tighter monogamy relations of entanglement measures based on fidelity." Laser Physics Letters 19, no. 8 (July 11, 2022): 085205. http://dx.doi.org/10.1088/1612-202x/ac772e.

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Abstract We study the Bures measure of entanglement and the geometric measure of entanglement as special cases of entanglement measures based on fidelity, and find their tighter monogamy inequalities over tri-qubit systems as well as multi-qubit systems. Furthermore, we derive the monogamy inequality of concurrence for qudit quantum systems by projecting higher-dimensional states to qubit substates.

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4

Gour, Gilad, and Yu Guo. "Monogamy of entanglement without inequalities." Quantum 2 (August 13, 2018): 81. http://dx.doi.org/10.22331/q-2018-08-13-81.

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We provide a fine-grained definition for monogamous measure of entanglement that does not invoke any particular monogamy relation. Our definition is given in terms an equality, as oppose to inequality, that we call the "disentangling condition". We relate our definition to the more traditional one, by showing that it generates standard monogamy relations. We then show that all quantum Markov states satisfy the disentangling condition for any entanglement monotone. In addition, we demonstrate that entanglement monotones that are given in terms of a convex roof extension are monogamous if they are monogamous on pure states, and show that for any quantum state that satisfies the disentangling condition, its entanglement of formation equals the entanglement of assistance. We characterize all bipartite mixed states with this property, and use it to show that the G-concurrence is monogamous. In the case of two qubits, we show that the equality between entanglement of formation and assistance holds if and only if the state is a rank 2 bipartite state that can be expressed as the marginal of a pure 3-qubit state in the W class.

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5

Tao, Yuan-Hong, Kai Zheng, Zhi-Xiang Jin, and Shao-Ming Fei. "Tighter Monogamy Relations for Concurrence and Negativity in Multiqubit Systems." Mathematics 11, no. 5 (February 26, 2023): 1159. http://dx.doi.org/10.3390/math11051159.

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The entanglement in multipartite quantum system is hard to characterize and quantify, although it has been intensively studied in bipartite systems. The monogamy of entanglement, as a special property of multipartite systems, shows the distribution of entanglement in the system. In this paper, we investigate the monogamy relations for multi-qubit systems. By using two entangled measures, namely the concurrence C and the negativity Nc, we establish tighter monogamy inequalities for their α-th power than those in all the existing ones. We also illustrate the tightness of our results for some classes of quantum states.

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6

Gao, Li-Min, Feng-Li Yan, and Ting Gao. "Monogamy of nonconvex entanglement measures." Results in Physics 31 (December 2021): 104983. http://dx.doi.org/10.1016/j.rinp.2021.104983.

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7

Gour, Gilad, Somshubhro Bandyopadhyay, and Barry C. Sanders. "Dual monogamy inequality for entanglement." Journal of Mathematical Physics 48, no. 1 (January 2007): 012108. http://dx.doi.org/10.1063/1.2435088.

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8

WEI, TZU-CHIEH. "MONOGAMY OF ENTANGLEMENT, N-REPRESENTABILITY PROBLEMS AND GROUND STATES." International Journal of Modern Physics B 26, no. 27n28 (September 18, 2012): 1243014. http://dx.doi.org/10.1142/s021797921243014x.

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Monogamy of entanglement is a quantum mechanical property that limits quantum correlations shared among many parties. In an example strongly interacting spin system we examine approaches for approximating the ground state energy both from above and below by mean-field and N-representability methods, respectively. Due to strong competition among the terms in the Hamiltonian, the resulting ground-state wavefunction, although is entangled, does not possess entanglement that is proportional to the system size, thus obeying the monogamy of entanglement.

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9

Liu, Feng. "Monogamy Relations for Squared Entanglement Negativity." Communications in Theoretical Physics 66, no. 4 (October 1, 2016): 407–10. http://dx.doi.org/10.1088/0253-6102/66/4/407.

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10

Kim, Jeong San, and Barry C. Sanders. "Unified entropy, entanglement measures and monogamy of multi-party entanglement." Journal of Physics A: Mathematical and Theoretical 44, no. 29 (June 20, 2011): 295303. http://dx.doi.org/10.1088/1751-8113/44/29/295303.

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11

Yu, Chang-shui, and He-shan Song. "Monogamy and entanglement in tripartite quantum states." Physics Letters A 373, no. 7 (February 2009): 727–30. http://dx.doi.org/10.1016/j.physleta.2008.12.058.

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12

Yang, Dong. "A simple proof of monogamy of entanglement." Physics Letters A 360, no. 2 (December 2006): 249–50. http://dx.doi.org/10.1016/j.physleta.2006.08.027.

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13

Jha, Abhishek Kumar, Supratik Mukherjee, and Bindu A. Bambah. "Tri-partite entanglement in neutrino oscillations." Modern Physics Letters A 36, no. 09 (February 22, 2021): 2150056. http://dx.doi.org/10.1142/s0217732321500565.

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We investigate and quantify bipartite and tripartite entanglement measures in two- and three-flavor neutrino oscillations. The bipartite entanglement is analogous to the entanglement swapping resulting from a beam splitter in quantum optics. We calculate various entanglement measures, such as the concurrence, negativity, and three-tangle for the three-neutrino system. The significant result is that a monogamy inequality in terms of negativity leads to a residual entanglement, implying genuine tripartite entanglement in the three-neutrino system. We establish an analogy of the three-neutrino state with a generalized W-state class in quantum optics.

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14

Qin, Meng, Xin Zhang, and Zhong-Zhou Ren. "Renormalization of quantum deficit and monogamy relation in the Heisenberg XXZ model." Quantum Information and Computation 16, no. 9&10 (July 2016): 835–44. http://dx.doi.org/10.26421/qic16.9-10-6.

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In this study, the dynamical behavior of quantum deficit and monogamy relation in the Heisenberg XXZ model is investigated by implementing quantum renormalization group theory. The results demonstrate that the quantum deficit can be used to capture the quantum phase transitions point and show scaling behavior with the spin chain size increasing. It was also found that the critical exponent has no change when varying measure from entanglement to quantum correlation. The monogamy relation is influenced by the steps of quantum renormalization group and the ways of splitting the block states. Furthermore, the monogamy relation of generalized W state also is given by means of quantum deficit.

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15

Johnston, Nathaniel, Rajat Mittal, Vincent Russo, and John Watrous. "Extended non-local games and monogamy-of-entanglement games." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2189 (May 2016): 20160003. http://dx.doi.org/10.1098/rspa.2016.0003.

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We study a generalization of non-local games—which we call extended non-local games —in which the players, Alice and Bob, initially share a tripartite quantum state with the referee. In such games, the winning conditions for Alice and Bob may depend on the outcomes of measurements made by the referee, on its part of the shared quantum state, in addition to Alice and Bob's answers to randomly selected questions. Our study of this class of games was inspired by the monogamy-of-entanglement games introduced by Tomamichel, Fehr, Kaniewski and Wehner, which they also generalize. We prove that a natural extension of the Navascués–Pironio–Acín hierarchy of semidefinite programmes converges to the optimal commuting measurement value of extended non-local games, and we prove two extensions of results of Tomamichel et al. concerning monogamy-of-entanglement games.

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16

Mardari, Ghenadie. "How to Erase Quantum Monogamy?" Quantum Reports 3, no. 1 (January 21, 2021): 53–67. http://dx.doi.org/10.3390/quantum3010004.

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The phenomenon of quantum erasure exposed a remarkable ambiguity in the interpretation of quantum entanglement. On the one hand, the data is compatible with the possibility of arrow-of-time violations. On the other hand, it is also possible that temporal non-locality is an artifact of post-selection. Twenty years later, this problem can be solved with a quantum monogamy experiment, in which four entangled quanta are measured in a delayed-choice arrangement. If Bell violations can be recovered from a “monogamous” quantum system, then the arrow of time is obeyed at the quantum level.

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17

Gao, Li-Min, Feng-Li Yan та Ting Gao. "Tighter monogamy relations of multiqubit entanglement in terms of Rényi-α entanglement". Communications in Theoretical Physics 72, № 8 (15 липня 2020): 085102. http://dx.doi.org/10.1088/1572-9494/ab7ece.

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18

Culf, Eric, and Thomas Vidick. "A monogamy-of-entanglement game for subspace coset states." Quantum 6 (September 1, 2022): 791. http://dx.doi.org/10.22331/q-2022-09-01-791.

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We establish a strong monogamy-of-entanglement property for subspace coset states, which are uniform superpositions of vectors in a linear subspace of F2n to which has been applied a quantum one-time pad. This property was conjectured recently by [Coladangelo, Liu, Liu, and Zhandry, Crypto'21] and shown to have applications to unclonable decryption and copy-protection of pseudorandom functions. We present two proofs, one which directly follows the method of the original paper and the other which uses an observation from [Vidick and Zhang, Eurocrypt'20] to reduce the analysis to a simpler monogamy game based on BB'84 states. Both proofs ultimately rely on the same proof technique, introduced in [Tomamichel, Fehr, Kaniewski and Wehner, New Journal of Physics '13].

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19

Gao, L., M. Junge, and N. Laracuente. "Heralded channel Holevo superadditivity bounds from entanglement monogamy." Journal of Mathematical Physics 59, no. 6 (June 2018): 062203. http://dx.doi.org/10.1063/1.5011660.

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20

Kim, Jeong San, and Barry C. Sanders. "Monogamy of multi-qubit entanglement using Rényi entropy." Journal of Physics A: Mathematical and Theoretical 43, no. 44 (October 18, 2010): 445305. http://dx.doi.org/10.1088/1751-8113/43/44/445305.

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21

Yu, Chang-shui, Dong-mo Li, and Nan-nan Zhou. "Monogamy of finite-dimensional entanglement induced by coherence." EPL (Europhysics Letters) 125, no. 5 (April 9, 2019): 50001. http://dx.doi.org/10.1209/0295-5075/125/50001.

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22

Liang, Yanying, Chuan-Jie Zhu, and Zhu-Jun Zheng. "Tighter Monogamy Constraints in Multi-Qubit Entanglement Systems." International Journal of Theoretical Physics 59, no. 4 (February 26, 2020): 1291–305. http://dx.doi.org/10.1007/s10773-020-04406-3.

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23

Adesso, G., and I. Fuentes-Schuller. "Correlation loss and multipartite entanglement across a black hole horizon (." Quantum Information and Computation 9, no. 7&8 (July 2009): 657–65. http://dx.doi.org/10.26421/qic9.7-8-8.

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We investigate the Hawking effect on entangled fields. By considering a scalar field which is in a two-mode squeezed state from the point of view of freely falling (Kruskal) observers crossing the horizon of a Schwarzschild black hole, we study the degradation of quantum and classical correlations in the state from the perspective of physical (Schwarzschild) observers confined outside the horizon. Due to monogamy constraints on the entanglement distribution, we show that the lost bipartite entanglement is recovered as multipartite entanglement among modes inside and outside the horizon. In the limit of a small-mass black hole, no bipartite entanglement is detected outside the horizon, while the genuine multipartite entanglement interlinking the inner and outer regions grows infinitely.

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24

Leggio, Bruno, Anna Napoli, Hiromichi Nakazato, and Antonino Messina. "Bounds on Mixed State Entanglement." Entropy 22, no. 1 (January 1, 2020): 62. http://dx.doi.org/10.3390/e22010062.

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In the general framework of d 1 × d 2 mixed states, we derive an explicit bound for bipartite negative partial transpose (NPT) entanglement based on the mixedness characterization of the physical system. The derived result is very general, being based only on the assumption of finite dimensionality. In addition, it turns out to be of experimental interest since some purity-measuring protocols are known. Exploiting the bound in the particular case of thermal entanglement, a way to connect thermodynamic features to the monogamy of quantum correlations is suggested, and some recent results on the subject are given a physically clear explanation.

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25

Geetha, P. J., Sudha, and K. S. Mallesh. "Comparative analysis of entanglement measures based on monogamy inequality." Chinese Physics B 26, no. 5 (May 2017): 050301. http://dx.doi.org/10.1088/1674-1056/26/5/050301.

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26

Luo, Yu, та Yongming Li. "Monogamy of αth power entanglement measurement in qubit systems". Annals of Physics 362 (листопад 2015): 511–20. http://dx.doi.org/10.1016/j.aop.2015.08.022.

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27

ZHAO, MING-JING, SHAO-MING FEI, and ZHI-XI WANG. "ENTANGLEMENT PROPERTY AND MONOGAMY RELATION OF GENERALIZED MIXED W STATES." International Journal of Quantum Information 08, no. 06 (September 2010): 905–12. http://dx.doi.org/10.1142/s0219749910006216.

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We introduce a new class of multipartite entangled mixed states with pure state decompositions of generalized W states, similar to Schmidt-correlated states having generalized GHZ states in the pure state decomposition. The entanglement and separability properties are studied according to PPT operations. Monogamy relations linked to these states are also investigated.

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28

Guo, Yu. "When Is a Genuine Multipartite Entanglement Measure Monogamous?" Entropy 24, no. 3 (February 28, 2022): 355. http://dx.doi.org/10.3390/e24030355.

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A crucial issue in quantum communication tasks is characterizing how quantum resources can be quantified and distributed over many parties. Consequently, entanglement has been explored extensively. However, there are few genuine multipartite entanglement measures and whether it is monogamous is so far unknown. In this work, we explore the complete monogamy of genuine multipartite entanglement measure (GMEM) for which, at first, we investigate a framework for unified/complete GMEM according to the unified/complete multipartite entanglement measure we proposed in 2020. We find a way of inducing unified/complete GMEM from any given unified/complete multipartite entanglement measure. It is shown that any unified GMEM is completely monogamous, and any complete GMEM that is induced by given complete multipartite entanglement measure is completely monogamous. In addition, the previous GMEMs are checked under this framework. It turns out that the genuinely multipartite concurrence is not as good of a candidate as GMEM.

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29

DAOUD, M., R. AHL LAAMARA, and R. ESSABER. "QUANTUM CORRELATIONS DYNAMICS OF QUASI-BELL CAT STATES." International Journal of Quantum Information 11, no. 06 (September 2013): 1350057. http://dx.doi.org/10.1142/s0219749913500573.

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A model of dynamics of quantum correlations of two modes quasi-Bell cat states, based on Glauber coherent states, is considered. The analytic expressions of pairwise entanglement of formation, quantum discord and its geometrized variant are explicitly derived. We analyze the distribution of quantum correlations between the two modes and the environment. We show that, in contrast with squared concurrence, entanglement of formation, quantum discord and geometric quantum discord do not follow the property of monogamy except in some particular situations that we discuss.

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30

Baba, H., W. Kaydi, M. Daoud, and M. Mansour. "Entanglement of formation and quantum discord in multipartite j-spin coherent states." International Journal of Modern Physics B 34, no. 26 (October 2, 2020): 2050237. http://dx.doi.org/10.1142/s0217979220502379.

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We study the entanglement of formation and the quantum discord contained in even and odd multipartite [Formula: see text]-spin coherent states. The key element of this investigation is the fact that a single [Formula: see text]-spin coherent state is viewed as comprising [Formula: see text] qubit states. We compute the quantum correlations present in the n even and odd [Formula: see text]-spin coherent states by considering all possible bipartite splits of the multipartite system. We discuss the different bi-partition schemes of quantum systems and we examine in detail the conservation rules governing the distribution of quantum correlations between the different qubits of the multipartite system. Finally, we derive the explicit expressions of quantum correlations present in even and odd spin coherent states decomposed in four spin sub-systems. We also analyze the properties of monogamy and we show in particular that the entanglement of the formation and the quantum discord obey the relation of monogamy only for even multipartite [Formula: see text]-spin coherent states.

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31

Shi, Xian. "Monogamy relations of quantum entanglement for partially coherently superposed states." Chinese Physics B 26, no. 12 (December 2017): 120303. http://dx.doi.org/10.1088/1674-1056/26/12/120303.

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32

Yu, Long-Bao, Li-Hua Zhang, Jun-Long Zhao, and Yong-Sheng Tang. "Comment on ‘Monogamy of multi-qubit entanglement using Rényi entropy’." Journal of Physics A: Mathematical and Theoretical 51, no. 8 (January 30, 2018): 088001. http://dx.doi.org/10.1088/1751-8121/aa9d04.

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33

Jin, Zhi-Xiang, Shao-Ming Fei, and Xianqing Li-Jost. "Generalized Entanglement Monogamy and Polygamy Relations for N-Qubit Systems." International Journal of Theoretical Physics 58, no. 5 (February 18, 2019): 1576–89. http://dx.doi.org/10.1007/s10773-019-04053-3.

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34

ADESSO, GERARDO, and FABRIZIO ILLUMINATI. "ENTANGLEMENT SHARING: FROM QUBITS TO GAUSSIAN STATES." International Journal of Quantum Information 04, no. 03 (June 2006): 383–93. http://dx.doi.org/10.1142/s0219749906001852.

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It is a central trait of quantum information theory that there exist limitations to the free sharing of quantum correlations among multiple parties. Such monogamy constraints have been introduced in a landmark paper by Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a trade-off between the couplewise and the genuine tripartite entanglement for states of three qubits. Since then, a lot of efforts have been devoted to the investigation of distributed entanglement in multipartite quantum systems. In this paper we report, in a unifying framework, a bird's eye view of the most relevant results that have been established so far on entanglement sharing in quantum systems. We will take off from the domain of N qubits, graze qudits, and finally land in the almost unexplored territory of multimode Gaussian states of continuous variable systems.

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35

Hayden, Patrick, Peter W. Shor, and Andreas Winter. "Random Quantum Codes from Gaussian Ensembles and an Uncertainty Relation." Open Systems & Information Dynamics 15, no. 01 (March 2008): 71–89. http://dx.doi.org/10.1142/s1230161208000079.

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Using random Gaussian vectors and an information-uncertainty relation, we give a proof that the coherent information is an achievable rate for entanglement transmission through a noisy quantum channel. The codes are random subspaces selected according to the Haar measure, but distorted as a function of the sender's input density operator. Using large deviations techniques, we show that classical data transmitted in either of two Fourier-conjugate bases for the coding subspace can be decoded with low probability of error. A recently discovered information-uncertainty relation then implies that the quantum mutual information for entanglement encoded into the subspace and transmitted through the channel will be high. The monogamy of quantum correlations finally implies that the environment of the channel cannot be significantly coupled to the entanglement which, concluding, ensures the existence of a decoding by the receiver.

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36

D'Ariano, G. M., F. Manessi, P. Perinotti, and A. Tosini. "Fermionic computation is non-local tomographic and violates monogamy of entanglement." EPL (Europhysics Letters) 107, no. 2 (July 1, 2014): 20009. http://dx.doi.org/10.1209/0295-5075/107/20009.

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37

Jin, Zhi-Xiang, and Cong-Feng Qiao. "Monogamy and polygamy relations of multiqubit entanglement based on unified entropy." Chinese Physics B 29, no. 2 (February 2020): 020305. http://dx.doi.org/10.1088/1674-1056/ab6720.

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38

Ren, Xi-Jun, and Yanni Shi. "A stronger entanglement monogamy inequality in a 2⊗2⊗3 system." Journal of Physics A: Mathematical and Theoretical 43, no. 39 (August 23, 2010): 395301. http://dx.doi.org/10.1088/1751-8113/43/39/395301.

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39

Bryan, K. L. H., and A. J. M. Medved. "Black Holes and Information: A New Take on an Old Paradox." Advances in High Energy Physics 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/7578462.

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Анотація:

Interest in the black hole information paradox has recently been catalyzed by the newer “firewall” argument. The crux of the updated argument is that previous solutions which relied on observer complementarity are in violation of the quantum condition of monogamy of entanglement, with the prescribed remedy being to discard the equivalence principle in favor of an energy barrier (or firewall) at the black hole horizon. Differing points of view have been put forward, including the “ER = EPR” counterargument and the final-state solution, both of which can be viewed as potential resolutions to the apparent conflict between quantum monogamy and Einstein equivalence. After reviewing these recent developments, this paper argues that the ER = EPR and final-state solutions can—thanks to observer complementarity—be seen as the same resolution of the paradox but from two different perspectives: inside and outside the black hole.

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40

Zong, Xiao-Lan, Hao-Hao Yin, Wei Song, and Zhuo-Liang Cao. "Monogamy of Quantum Entanglement." Frontiers in Physics 10 (June 9, 2022). http://dx.doi.org/10.3389/fphy.2022.880560.

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Анотація:

Unlike classical correlation, quantum entanglement cannot be freely shared among many parties. This restricted shareability of entanglement among multi-party systems is known as monogamy of entanglement, which is one of the most fundamental properties of entanglement. Here, we summarize recent theoretical progress in the field of monogamy of entanglement. We firstly review the standard CKW-type monogamy inequalities in terms of various entanglement measures. In particular, the squashed entanglement and one-way distillable entanglement are monogamous for arbitrary dimensional systems. We then introduce some generalized version of monogamy inequalities which extend and sharpen the traditional ones. We also consider the dual polygamy inequalities for multi-party systems. Moreover, we present two new definitions to define monogamy of entanglement. Finally, some challenges and future directions for monogamy of entanglement are highlighted.

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41

Sun, Qi, Tao Li, Zhi-Xiang Jin, and Deng-Feng Liang. "Unified entropy entanglement with tighter constraints on multipartite systems." Chinese Physics B, November 17, 2022. http://dx.doi.org/10.1088/1674-1056/aca399.

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Abstract Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide a characterization of multiqubit entanglement constraints in terms of unified-$(q,s)$ entropy. A class of tighter monogamy inequalities of multiqubit entanglement based on the $\alpha$-th power of unified-$(q,s)$ entanglement for $\alpha\geq 1$ and a class of polygamy inequalities in terms of the $\beta$-th power of unified-$(q,s)$ entanglement of assistance are established in this paper. Our results present a general class of the monogamy and polygamy relations for bipartite entanglement measures based on unified-$(q,s)$ entropy, which are tighter than the existing ones. What's more, some usual monogamy and polygamy relations, such as monogamy and polygamy relations based on entanglement of formation, Renyi-$q$ entanglement of assistance and Tsallis-$q$ entanglement of assistance, can be obtained from these results by choosing appropriate parameters $(q,s)$ in unified-$(q,s)$ entropy entanglement. Typical examples are also presented for illustration.

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42

Zhang, Jia-Bin, Tao Li, and Zhi-Xi Wang. "Product-form monogamy relations of entanglement in multiqubit systems." International Journal of Quantum Information, August 20, 2021, 2150022. http://dx.doi.org/10.1142/s0219749921500222.

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Анотація:

Monogamy relations of entanglement play an important role in quantum systems, however, most of them are given in summation form. In this paper, we investigate the product-form monogamy relations of multipartite entanglement in terms of the [Formula: see text]th power of concurrence and negativity. Compared with the existing monogamy relations, the product-form monogamy relations of multi-body quantum entanglement have a stricter lower bound.

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43

Khan, Awais, Junaid ur Rehman, Kehao Wang, and Hyundong Shin. "Unified Monogamy Relations of Multipartite Entanglement." Scientific Reports 9, no. 1 (November 11, 2019). http://dx.doi.org/10.1038/s41598-019-52817-y.

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Анотація:

Abstract Unified-(q, s) entanglement $$({{\mathscr{U}}}_{q,s})$$ ( U q , s ) is a generalized bipartite entanglement measure, which encompasses Tsallis-q entanglement, Rényi-q entanglement, and entanglement of formation as its special cases. We first provide the extended (q; s) region of the generalized analytic formula of $${{\mathscr{U}}}_{q,s}$$ U q , s . Then, the monogamy relation based on the squared $${{\mathscr{U}}}_{q,s}$$ U q , s for arbitrary multiqubit mixed states is proved. The monogamy relation proved in this paper enables us to construct an entanglement indicator that can be utilized to identify all genuine multiqubit entangled states even the cases where three tangle of concurrence loses its efficiency. It is shown that this monogamy relation also holds true for the generalized W-class state. The αth power $${{\mathscr{U}}}_{q,s}$$ U q , s based general monogamy and polygamy inequalities are established for tripartite qubit states.

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44

Kim, Jeong San. "Entanglement of formation and monogamy of multi-party quantum entanglement." Scientific Reports 11, no. 1 (January 27, 2021). http://dx.doi.org/10.1038/s41598-021-82052-3.

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Анотація:

AbstractWe provide a sufficient condition for the monogamy inequality of multi-party quantum entanglement of arbitrary dimensions in terms of entanglement of formation. Based on the classical–classical–quantum(ccq) states whose quantum parts are obtained from the two-party reduced density matrices of a three-party quantum state, we show the additivity of the mutual information of the ccq states guarantees the monogamy inequality of the three-party pure state in terms of EoF. After illustrating the result with some examples, we generalize our result of three-party systems into any multi-party systems of arbitrary dimensions.

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45

de Oliveira, Thiago R., Marcio F. Cornelio, and Felipe F. Fanchini. "Monogamy of entanglement of formation." Physical Review A 89, no. 3 (March 24, 2014). http://dx.doi.org/10.1103/physreva.89.034303.

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46

Bai, Yan-Kui, Ming-Yong Ye, and Z. D. Wang. "Entanglement monogamy and entanglement evolution in multipartite systems." Physical Review A 80, no. 4 (October 15, 2009). http://dx.doi.org/10.1103/physreva.80.044301.

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47

Yang, Xue, and Ming-Xing Luo. "Unified monogamy relation of entanglement measures." Quantum Information Processing 20, no. 3 (March 2021). http://dx.doi.org/10.1007/s11128-021-03041-z.

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48

Allen, Grant W., and David A. Meyer. "Polynomial Monogamy Relations for Entanglement Negativity." Physical Review Letters 118, no. 8 (February 24, 2017). http://dx.doi.org/10.1103/physrevlett.118.080402.

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49

Hiroshima, Tohya, Gerardo Adesso, and Fabrizio Illuminati. "Monogamy Inequality for Distributed Gaussian Entanglement." Physical Review Letters 98, no. 5 (February 1, 2007). http://dx.doi.org/10.1103/physrevlett.98.050503.

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50

Lee, Soojoon, and Jungjoon Park. "Monogamy of entanglement and teleportation capability." Physical Review A 79, no. 5 (May 28, 2009). http://dx.doi.org/10.1103/physreva.79.054309.

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