Unified entropy entanglement with tighter constraints on multipartite systems
Qi Sun(孙琪)1, Tao Li(李陶)1,†, Zhi-Xiang Jin(靳志祥)2,‡, and Deng-Feng Liang(梁登峰)1
1 School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China; 2 School of Computer Science and Techonology, Dongguan University of Technology, Dongguan 523808, China
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- entropy. A class of tighter monogamy inequalities of multiqubit entanglement based on the -th power of unified- entanglement for and a class of polygamy inequalities in terms of the -th power of unified- 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- entropy, which are tighter than the existing ones. What is more, some usual monogamy and polygamy relations, such as monogamy and polygamy relations based on entanglement of formation, Renyi- entanglement of assistance and Tsallis- entanglement of assistance, can be obtained from these results by choosing appropriate parameters in unified- entropy entanglement. Typical examples are also presented for illustration.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12175147, 11847209, and 11675113), the Natural Science Foundation of Beijing (Grant No. KZ201810028042), and Beijing Natural Science Foundation (Grant No. Z190005).
Corresponding Authors:
Tao Li, Zhi-Xiang Jin
E-mail: litao@btbu.edu.cn;jzxjinzhixiang@126.com
Cite this article:
Qi Sun(孙琪), Tao Li(李陶), Zhi-Xiang Jin(靳志祥), and Deng-Feng Liang(梁登峰) Unified entropy entanglement with tighter constraints on multipartite systems 2023 Chin. Phys. B 32 030304
[1] Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) [2] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys.81 865 [3] Mintert F, Kuś M and Buchleitner A 2004 Phys. Rev. Lett.92 167902 [4] Chen K, Albeverio S and Fei S M 2005 Phys. Rev. Lett.95 040504 [5] Breuer H P 2006 J. Phys. A: Math. Gen.39 11847 [6] Breuer H P 2006 Phys. Rev. Lett.97 080501 [7] de Vicente J I 2007 Phys. Rev. A75 052320 [8] Zhang C J, Zhang Y S, Zhang S and Guo G C 2007 Phys. Rev. A76 012334 [9] Coffman V, Kundu J and Wootters W K 2000 Phys. Rev. A61 052306 [10] Osborne T J and Verstraete F 2006 Phys. Rev. Lett.96 220503 [11] Pawlowski M 2010 Phys. Rev. A82 032313 [12] Wootters W K 1998 Phys. Rev. Lett.80 2245 [13] Gour G, Meyer D A and Sanders B C 2005 Phys. Rev. A72 042329 [14] Goura G, Bandyopadhyayb S and Sandersc B C 2007 J. Math. Phys.48 012108 [15] Kim J S 2010 Phys. Rev. A81 062328 [16] Kim J S and Sanders B C 2011 J. Phys. A: Math. Theor.44 295303 [17] Zhu X N and Fei S M 2014 Phys. Rev. A90 024304 [18] Jin Z X and Fei S M 2017 Quantum Inf. Process.16 77 [19] Kim J S 2018 Phys. Rev. A97 012334 [20] Jin Z X, Li J, Li T and Fei S M 2018 Phys. Rev. A97 032336 [21] Jin Z X and Fei S M 2019 Phys. Rev. A99 032343 [22] Guo M L, Li B, Wang Z X and Fei S M 2020 Chin. Phys. B29 070304 [23] Kim J S 2018 Sci. Rep.8 12245 [24] Jin Z X and Qiao C F 2020 Chin. Phys. B29 020305 [25] Hu X and Ye Z 2006 J. Math. Phys.47 023502 [26] Rastegin A E 2011 J. Stat. Phys.143 1120 [27] Kim J S 2012 Phys. Rev. A85 032335 [28] Rastegin A E 2012 J. Phys. A: Math. Theor.45 045302 [29] Rastegin A E 2013 J. Phys. A: Math. Theor.46 285301 [30] Liu Z W, Lloyd S and Zhu E 2018 J. High Energ. Phys.2018 41 [31] Luo Y, Zhang F G and Li Y 2017 Sci. Rep.7 1122 [32] Horodecki R, Horodecki P and Horodecki M 1996 Phys. Lett. A210 377 [33] Kim J S and Sanders B C 2010 J. Phys. A: Math. Theor.43 445305 [34] Tsallis C 1998 J. Stat. Phys.52 479
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
