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Much attention has been paid to the dynamics of quantum correlation in an open quantum system coupled to a single-layered environment for a long time. However, the system can be influenced by the multilayer environment or hierarchical environment in realistic scenarios, which is attracting increasing interest at present. In this context, we explore in this paper the dynamics of quantum correlation for a quantum system consisting of three independent qubits, each being immersed in a single mode lossy cavity which is further connected to another cavity. The influences of cavity-cavity coupling strength Ω and the decay rate of cavity Γ1 on the measures of quantum correlation, including negativity, Bell non-locality as well as entanglement witness, are investigated in detail in a strong coupling regime and a weak coupling regime. It is shown that the phenomena of sudden death and sudden birth can happen to both Bell non-locality and entanglement witness. When the decay rate Γ1 = 0 is given, with the increase of Ω these measures eventually reach their stationary values over time after a short period of damping oscillations, in which these stationary values will become larger for the larger Ω. At the same time, the values or the survival times of quantum correlation considered by us in the weak coupling regime are better than in the strong coupling case. In addition, the non-zero Γ1 has a great negative effect on quantum correlation. Hence, in order to suppress the loss of quantum correlation better, the effective manipulation of quantum weak measurement and measurement reversal operator is considered further. Some interesting results are obtained.
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Keywords:
- quantum entanglement /
- Bell non-locality /
- entanglement witness /
- weak measurement
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图 1 耦合强度
$\varOmega $ 取不同值时, 负性纠缠度${N_3}$ 、Bell非定域性$\left| {\left\langle {{B}} \right\rangle } \right| - 1$ 和纠缠目击$ - {\rm{EWs}}$ 在强耦合体系$g = 0.5\varGamma $ ((a)—(c))和弱耦合体系$g = 0.2\varGamma $ ((d)—(f))下随无量纲时间$\varGamma t$ 的变化曲线. 其中,${\varGamma _1} = 0$ Figure 1. Time evolution of Negativity
${N_3}$ , Bell non-locality$\left| {\left\langle {{B}} \right\rangle } \right| - 1$ and entanglement witnesses$ - {\rm{EWs}}$ as the function of dimensionless time$\varGamma t$ for the different values of coupling strength$\varOmega $ in the strong coupling regime$g = 0.5\varGamma $ ((a)–(c)) and the weak coupling regime$g = 0.2\varGamma $ ((d)–(f)) with${\varGamma _1} = 0$ .
图 2 耦合强度
$\varOmega $ 和弱测量强度m取不同值时, 负性纠缠度$N_3$ 在强耦合体系$g = 0.5\varGamma $ ((a)和(c))和弱耦合体系$g = 0.2\varGamma $ ((b)和(d))下随无量纲时间$\varGamma t$ 的变化曲线. 其中,${\varGamma _1} = 0$ Figure 2. Negativity
$N_3$ versus dimensionless time$\varGamma t$ for the different values of coupling strength$\varOmega $ and the weak measurement strength$m$ in the strong coupling regime$g = 0.5\varGamma $ ((a) and (c)) and the weak coupling regime$g = 0.2\varGamma $ ((b) and (d)) with${\varGamma _1} = 0$ .
图 3 Bell函数
$\left| {\left\langle {{B}} \right\rangle } \right| - 1$ 在强耦合体系$g = 0.5\varGamma $ ((a)和(c))和弱耦合体系$g = 0.2\varGamma $ ((b)和(d))下随无量纲时间$\varGamma t$ 的变化曲线. 其他参数取值与图2相同Figure 3. The change of Bell function
$\left| {\left\langle {{B}} \right\rangle } \right| - 1$ as a function of$\varGamma t$ in the strong coupling regime$g = 0.5\varGamma $ ((a) and (c)) and the weak coupling regime$g = 0.2\varGamma $ ((b) and (d)). The values of other parameters are the same as those in Fig. 2.
图 5 量子关联在强耦合体系
$g = 0.5\varGamma $ ((a)和(c))和弱耦合体系$g = 0.2\varGamma $ ((b)和(d))下的变化曲线. 其中, (a)和(b)无弱测量操作, (c)和(d)有弱测量操作. 参数$\varOmega = \varGamma $ 和${\varGamma _1} = 0.25\varGamma $ Figure 5. Change curves of quantum correlation in the strong coupling regime
$g = 0.5\varGamma $ ((a) and (c)) and the weak coupling regime$g = 0.2\varGamma $ ((b) and (d)), where (a) and (b) are the cases without measurement, while (c) and (d) are the cases with measurement. The parameters$\varOmega $ and${\varGamma _1}$ are set to$\varGamma $ and$0.25\varGamma $ , respectively. -
[1] Paneru D, Cohen E, Fickler R, Boyd R W, Karimi E 2020 Rep. Prog. Phys. 83 064001
Google Scholar
[2] Su Z F, Tan H S, Li X Y 2020 Phys. Rev. A 101 042112
Google Scholar
[3] Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
Google Scholar
[4] Kura N, Ueda M 2020 Phys. Rev. Lett. 124 010507
Google Scholar
[5] Hu X M, Xing W B, Liu B H, Huang Y F, Li C F, Guo G C 2020 Phys. Rev. Lett. 125 090503
Google Scholar
[6] Sabín C, García-Alcaine G 2007 Eur. Phys. J. D 48 435
[7] Maity A G, Das D, Ghosal A, Roy A, Majumdar A S 2020 Phys. Rev. A 101 042340
Google Scholar
[8] Rosset D, Branciard C, Barnea T J, Pütz G, Brunner N, Gisin N 2016 Phys. Rev. Lett. 116 010403
Google Scholar
[9] Altintas F, Eryigit R 2010 Phys. Lett. A 374 4283
Google Scholar
[10] Anwer H, Nawareg M, Cabello A, Bourennane M 2019 Phys. Rev. A 100 022104
Google Scholar
[11] Shin D K, Henson B M, Hodgman S S, Wasak T, Chwedeńczuk J, Truscott A G 2019 Nature 10 4447
[12] Kuo W T, Akhtar A A, Arovas D P, You Y Z 2020 Phys. Rev. B 101 224202
Google Scholar
[13] 刑贵超, 夏云杰 2018 67 070301
Google Scholar
Xing G C, Xia Y J 2018 Acta Phys. Sin. 67 070301
Google Scholar
[14] Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404
Google Scholar
[15] López C E, Romero G, Lastra F, Solano E, Retamal J C 2008 Phys. Rev. Lett. 101 080503
Google Scholar
[16] Aguilar G H, Valdés-Hernández A, Davidovich L, Walborn S P, Souto Ribeiro P H 2014 Phys. Rev. Lett. 113 240501
Google Scholar
[17] Antonelli C, Shtaif M, Brodsky M 2011 Phys. Rev. Lett. 106 080404
Google Scholar
[18] Bellomo B, Lo Franco R, Compagno G 2007 Phys. Rev. Lett. 99 160502
Google Scholar
[19] Mohamed A B A, Eleuch H, Raymond Ooi C H 2019 Sci. Rep. 9 19632
Google Scholar
[20] Deordi G L, Vidiella-Barranco A 2020 Opt. Commun. 475 126233
Google Scholar
[21] Pramanik T, Cho Y W, Han S W, Lee S Y, Moon S, Kim Y S 2019 Phys. Rev. A 100 042311
Google Scholar
[22] Hu M L 2012 Ann. Phys. 327 2332
Google Scholar
[23] Weilenmann M, Dive B, Trillo D, Aguilar E A, Navascués M 2019 Phys. Rev. Lett. 124 200502
[24] Zhou Y 2020 Phys. Rev. A 101 012301
Google Scholar
[25] Hanson R, Dobrovitski V V, Feiguin A E, Gywat O, Awschalom D D 2008 Science 320 352
Google Scholar
[26] Man Z X, Xia Y J, Rosario L F 2015 Phys. Rev. A 92 012315
Google Scholar
[27] Basit A, Ali H, Badshah F, Zhang H Y, Ge G Q 2017 Laser Phys. Lett. 14 125202
Google Scholar
[28] Bai X M, Xue N T, Liu N, Li J Q, Liang J Q 2019 Ann. Phys. 531 1900098
Google Scholar
[29] Xu K, Zhang G F, Zhou Y, Liu W M 2020 J. Opt. Soc. Am. B 37 933
Google Scholar
[30] Kim Y S, Lee J C, Kwon O, Kim Y H 2012 Nat. Phys. 8 117
Google Scholar
[31] Korotkov A N, Keane K 2010 Phys. Rev. A 81 040103(R
Google Scholar
[32] He Z, Zeng H S 2020 Quantum Inf. Process. 19 299
Google Scholar
[33] Qiu L, Tang G, Yang X Q, Wang A 2014 Ann. Phys. 350 137
Google Scholar
[34] Groen J P, Ristè D, Tornberg L, Cramer J, Degroot P C, Picot T, Johansson G, Dicarlo L 2013 Phys. Rev. Lett. 111 090506
Google Scholar
[35] Man Z X, Xia Y J, Rosario L F 2015 Sci. Rep. 5 13843
Google Scholar
[36] Gühne O, Tóth G 2009 Phys. Rep. 474 1
Google Scholar
[37] Xiao X, Yao Y, Zhong W J, Li Y L, Xie Y M 2016 Phys. Rev. A 93 012307
Google Scholar
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