Transformation relation between coherence and entanglement for two-qubit states
doi: 10.1088/1674-1056/ac7454
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Abstract: Entanglement and coherence are two important resources in quantum information theory. A question naturally arises: Is there some connection between them? We prove that the entanglement of formation and the first-order coherence of two-qubit states satisfy an inequality relation. Two-qubit pure state reaches the upper bound of this inequality. A large number of randomly generated states are used to intuitively verify the complementarity between the entanglement of formation and the first-order coherence. We give the maximum accessible coherence of two-qubit states. Our research results will provide a reliable theoretical basis for conversion of the two quantum resources.
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Key words:
- entanglement /
- coherence /
- first-order coherence /
- entanglement of formation
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1. The regional map of entanglement of formation ( E) versus the first-order coherence ( C) in binary entropy for arbitrary two-qubit states. The upper bounds (purple line) are denoted by E + C = 1. The figure plots the entanglement of formation ( E) along the y-axis, and the C along the x-axis, for 50000 randomly generated two-qubit states.
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[1] Schrödinger E 1935 Proc. Cambridge Philos. Soc. 31 555 10.1017/S0305004100013554 doi: 10.1017/S0305004100013554 [2] Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881 10.1103/PhysRevLett.69.2881 doi: 10.1103/PhysRevLett.69.2881 [3] Bennett C H, Brassard G, Crpeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895 10.1103/PhysRevLett.70.1895 doi: 10.1103/PhysRevLett.70.1895 [4] Bennett C H, DiVincenzo D P, Shor P W, Smolin J A, Terhal B M, Wootters W K 2001 Phys. Rev. Lett. 87 077902 10.1103/PhysRevLett.87.077902 doi: 10.1103/PhysRevLett.87.077902 [5] Wootters W K 1998 Phys. Rev. Lett. 80 2245 10.1103/PhysRevLett.80.2245 doi: 10.1103/PhysRevLett.80.2245 [6] Uhlmann A 2000 Phys. Rev.A 62 032307 10.1103/PhysRevA.62.032307 doi: 10.1103/PhysRevA.62.032307 [7] Peres A 1996 Phys. Rev. Lett. 77 1413 10.1103/PhysRevLett.77.1413 doi: 10.1103/PhysRevLett.77.1413 [8] Piani M 2009 Phys. Rev. Lett. 103 160504 10.1103/PhysRevLett.103.160504 doi: 10.1103/PhysRevLett.103.160504 [9] Osterloh A, Amico L, Falci G, Fazio R 2002 Nature 416 608 10.1038/416608a doi: 10.1038/416608a [10] Mintert F, Kus M, Buchleitner A 2005 Phys. Rev. Lett. 95 260502 10.1103/PhysRevLett.95.260502 doi: 10.1103/PhysRevLett.95.260502 [11] Walborn S P, Souto Ribeiro P H, Davidovich L, Mintert F, Buchleitner A 2006 Nature 440 1022 10.1038/nature04627 doi: 10.1038/nature04627 [12] Fei S M, Zhao M J, Chen K, Wang Z X 2009 Phys. Rev.A 80 032320 10.1103/PhysRevA.80.032320 doi: 10.1103/PhysRevA.80.032320 [13] Li M, Fei S M 2012 Phys. Rev.A 85 014304 10.1103/PhysRevA.85.014304 doi: 10.1103/PhysRevA.85.014304 [14] Glauber and Roy J 1963 Phys. Rev. 130 2529 10.1103/PhysRev.130.2529 doi: 10.1103/PhysRev.130.2529 [15] Chin A W, Prior J, Rosenbach R, Caycedo-Soler F, Huelga S F, Plenio M B 2013 Nat. Phys. 9 113 10.1038/nphys2515 doi: 10.1038/nphys2515 [16] Lloyd S 2011 Phys. Conf. Ser. 302 012037 10.1088/1742-6596/302/1/012037 doi: 10.1088/1742-6596/302/1/012037 [17] Li C M, Lambert N, Chen Y N, Chen G Y, Nori F 2012 Sci. Rep. 2 885 10.1038/srep00885 doi: 10.1038/srep00885 [18] Huelga S F, Plenio M B 2013 Contemp. Phys. 54 181 10.1080/00405000.2013.829687 doi: 10.1080/00405000.2013.829687 [19] Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401 10.1103/PhysRevLett.113.140401 doi: 10.1103/PhysRevLett.113.140401 [20] Winter A, Yang D 2016 Phys. Rev. Lett. 116 120404 10.1103/PhysRevLett.116.120404 doi: 10.1103/PhysRevLett.116.120404 [21] Chitambar E, Hsieh M H 2016 Phys. Rev. Lett. 117 020402 10.1103/PhysRevLett.117.020402 doi: 10.1103/PhysRevLett.117.020402 [22] Yuan X, Zhou H, Cao Z, Ma X 2015 Phys. Rev.A 92 022124 10.1103/PhysRevA.92.022124 doi: 10.1103/PhysRevA.92.022124 [23] Chitambar E, Streltsov A, Rana S, Bera M N, Adesso G, Lewenstein M 2016 Phys. Rev. Lett. 116 070402 10.1103/PhysRevLett.116.070402 doi: 10.1103/PhysRevLett.116.070402 [24] Napoli C, Bromley T R, Cianciaruso M, Piani M, Johnston N, Adesso G 2016 Phys. Rev. Lett. 116 150502 10.1103/PhysRevLett.116.150502 doi: 10.1103/PhysRevLett.116.150502 [25] Svozilik J, Valles A, Perina J, Torres J P 2015 Phys. Rev. Lett. 115 220501 10.1103/PhysRevLett.115.220501 doi: 10.1103/PhysRevLett.115.220501 [26] Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403 10.1103/PhysRevLett.115.020403 doi: 10.1103/PhysRevLett.115.020403 [27] Singh U, Bera M N, Dhar H S, Pati A K 2015 Phys. Rev.A 91 052115 10.1103/PhysRevA.91.052115 doi: 10.1103/PhysRevA.91.052115 [28] Xi Z J, Li Y M, Fan H 2015 Sci. Rep. 5 10922 10.1038/srep10922 doi: 10.1038/srep10922 [29] Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403 10.1103/PhysRevLett.115.020403 doi: 10.1103/PhysRevLett.115.020403 [30] Winter A, Yang D 2016 Phys. Rev. Lett. 116 120404 10.1103/PhysRevLett.116.120404 doi: 10.1103/PhysRevLett.116.120404 [31] Chitambar E, Streltsov A, Rana S, Bera M N, Adesso G, Lewenstein M 2016 Phys. Rev. Lett. 116 070402 10.1103/PhysRevLett.116.070402 doi: 10.1103/PhysRevLett.116.070402 [32] Napoli C, Bromley T R, Cianciaruso M, Pinai M, Johnston N, Adesso G 2016 Phys. Rev. Lett. 116 150502 10.1103/PhysRevLett.116.150502 doi: 10.1103/PhysRevLett.116.150502 [33] Cernoch A, Bartkiewicz K, Lemr K, Soubusta J 2016 Phys. Rev.A 97 042305 10.1103/PhysRevA.97.042305 doi: 10.1103/PhysRevA.97.042305 [34] Bruschi D E, Sabin C, Paraoanu G S 2017 Phys. Rev.A 95 062324 10.1103/PhysRevA.95.062324 doi: 10.1103/PhysRevA.95.062324 [35] Bennett C H, DiVincenzo D P, Smolin J, Wootters W K 1996 Phys. Rev.A 54 3824 10.1103/PhysRevA.54.3824 doi: 10.1103/PhysRevA.54.3824 [36] Mandel L, Wolf E, Shapiro J H 1996 Phys. Today 49 68 10.1063/1.2807623 doi: 10.1063/1.2807623 [37] Fan X G, Sun W Y, Ding Z Y, et al. 2019 New J. Phys. 21 093053 10.1088/1367-2630/ab41b1 doi: 10.1088/1367-2630/ab41b1