-
The uncertainty principle which restricts the observer's ability to make precise measurements of two incompatible observables plays a crucial role in quantum precision measurement within the field of quantum information science. When quantum systems interact with their surroundings, they inevitably result in decoherence, which increases the uncertainty of the system. In the process of quantum information processing, the effective regulation of uncertainty becomes a key problem to be solved. In this work, we investigate the quantum-memory-assisted entropic uncertainty relation of a two-qubit system under correlated channels with dephasing colored noise. We demonstrate that it is possible to control the entropic uncertainty, denoted as U, and its lower bound, Ub, by combining correlations between successive uses of channels and the non-Markovianity of the dynamical evolution. Firstly, the evolutionary characteristics of the trace distance are employed to distinguish between Markovianity and non-Markovianity of the channel. Subsequently, the system is selected to be either a maximally entangled or separated state initially. By adjusting the strength of the correlations η, we find that with the increase of η, the entropic uncertainty and its lower bound decrease. Especially, if the channel is fully correlated (η = 1), the entropic uncertainty and its lower bound remain constant under the channel, indicating that decoherence is completely suppressed. A comparison of Markovian and non-Markovian channels reveals that the entropic uncertainty and its lower bound exhibit oscillatory behaviour under non-Markovian channels. The combination of correlations and non-Markovianity of the channel demonstrates that the entropic uncertainty and its lower bound can be reduced under fully correlated channels where the non-Markovianity has no effect. This is because fully correlated channels suppress decoherence to the greatest extent. Under partially correlated channels, the combination of correlations and non-Markovianity can result in a more effective reduction in the entropic uncertainty and its lower bound. Under such channels, correlations of the channel decrease the entropic uncertainty and its lower bound during the whole evolution, while the non-Markovianity contributes to the oscillations of them and reduce them in some specific time. Furthermore, the results show that the entropic uncertainty and its lower bound reach steady values that depend only on the strength of the correlations after long-time evolution. In other words, the stronger the correlations, the lower the entropic uncertainty and its lower bound of steady states. Finally, we analyse the physical nature of the decrease of the entropic uncertainty and its lower bound, and it is found that the decrease of the entropic uncertainty and its lower bound is due to the increase of the quantum correlations in the system.
-
Keywords:
- Uncertainty relation /
- Correlated channel /
- Non-Markovianity /
- Quantum correlation
-
图 1 迹距离TD随时间的演化, 纵坐标为TD的数值, 蓝色实线、黑色虚线线分别对应通道参数$ \nu=0.1 $和10
Figure 1. The evolution of the trace distance TD. Y-axis represents TD, and the blue solid curve and back dashed curve respectively correspond to $ \nu=0.1 $ and 10.
图 2 初态为最大纠缠态时熵不确定度U及其下限$ U_{b} $随时间的演化, 纵坐标为U或$ U_{b} $的数值, 蓝色、绿色、黑色、红色曲线分别对应关联强度$ \eta=0, 0.5, 0.8, 1 $, 通道参数$ \nu=0.1 $, 呈现马尔科夫性
Figure 2. The evolution of uncertainty U and its lower bound $ U_{b} $ of the system which is initially in a maximally entangled state. Y-axis represents U or $ U_{b} $, and blue, green, black and red curves correspond to η as 0, 0.5, 0.8, 1. The channel is Markovian, where $ \nu=0.1 $.
图 3 初态为最大纠缠态时熵不确定度U及其下限$ U_{b} $随时间的演化, 纵坐标为U或$ U_{b} $的数值, 蓝色、绿色、黑色、红色曲线分别对应关联强度$ \eta=0, 0.5, 0.8, 1 $, 通道参数$ \nu=10 $, 呈现非马尔科夫性
Figure 3. The evolution of uncertainty U and its lower bound $ U_{b} $ of the system which is initially in a maximally entangled state. Y-axis represents U or $ U_{b} $, and blue, green, black and red curves correspond to η as 0, 0.5, 0.8, 1. The channel is non-Markovian, where $ \nu=10 $.
图 4 初态为可分离态时熵不确定度U及其下限$ U_{b} $随时间的演化, 纵坐标为U或$ U_{b} $的数值, 蓝色、绿色、黑色、红色曲线分别对应关联强度$ \eta=0, 0.5, 0.8, 1 $, 实线代表熵不确定度U, 虚线代表下限$ U_{b} $. 通道参数$ \nu=0.1 $, 呈现马尔科夫性
Figure 4. The evolution of uncertainty U and its lower bound $ U_{b} $ of the system which is initially in a separated state. Y-axis represents U or $ U_{b} $, and blue, green, black and red curves correspond to η as 0, 0.5, 0.8, 1. The solid curves represent uncertainty U, and the dashed curves represent its lower bound $ U_{b} $. The channel is Markovian, where $ \nu=0.1 $.
图 5 初态为可分离态时熵不确定度U及其下限$ U_{b} $随时间的演化, 纵坐标为U或$ U_{b} $的数值, 蓝色、绿色、黑色、红色曲线分别对应关联强度$ \eta=0, 0.5, 0.8, 1 $, 实线代表熵不确定度U, 虚线代表下限$ U_{b} $. 通道参数$ \nu=10 $, 呈现非马尔科夫性
Figure 5. The evolution of uncertainty U and its lower bound $ U_{b} $ of the system which is initially in a separated state. Y-axis represents U or $ U_{b} $, and blue, green, black and red curves correspond to η as 0, 0.5, 0.8, 1. The solid curves represent uncertainty U, and the dashed curves represent its lower bound $ U_{b} $. The channel is non-Markovian, where $ \nu=10 $.
图 6 初态为可分离态时量子关联$ Q(\rho_{AB}) $随时间的演化, 纵坐标为$ Q(\rho_{AB}) $的数值, 蓝色、绿色、黑色、红色曲线分别对应关联强度$ \eta=0, 0.5, 0.8, 1 $. (a)通道参数$ \nu= $$ 0.1 $, 呈现马尔科夫性; (b)通道参数$ \nu=10 $, 呈现非马尔科夫性
Figure 6. The evolution of quantum correlations $ Q(\rho_{AB}) $ of the system which is initially in a separated state. Y-axis represents $ Q(\rho_{AB}) $, and blue, green, black and red curves correspond to η as 0, 0.5, 0.8. (a) The channel is Markovian, where $ \nu=0.1 $; (b) The channel is non-Markovian, where $ \nu=10 $.
-
[1] Heisenberg W 1927 Z. Phys. 43 172
Google Scholar
[2] Robertson H P 1929 Phys. Rev. 34 163
Google Scholar
[3] Deutsch D 1983 Phys. Rev. Lett. 50 631
Google Scholar
[4] Kraus K 1987 Phys. Rev. D 35 3070
Google Scholar
[5] Maassen H, Uffink J B M 1988 Phys. Rev. Lett. 60 1103
Google Scholar
[6] Berta M, Christandl M, Colbeck R, Renes J M and Renner R 2010 Nat. Phys. 6 659
Google Scholar
[7] Prevedel R, Hamel D R, Colbeck R, Fisher K and Resch K J 2011 Nat. Phys. 7 757
Google Scholar
[8] Li C F, Xu J S, Xu X Y, Li K and Guo G C 2011 Nat. Phys. 7 752
Google Scholar
[9] Shi J, Ding Z, Wu T, He J, Yu L, Sun W, Wang D and Ye L 2017 Laser Phys. Lett. 14 125208
Google Scholar
[10] Hall M J W, Cerf N J 2012 New J. Phys. 14 033040
Google Scholar
[11] Ekert A K 1991 Phys. Rev. Lett 67 661
Google Scholar
[12] Renes J M, Boileau J C 2009 Phys. Rev. Lett 103 020402
Google Scholar
[13] Haseli S, Dolatkhah H, Rangani Jahromi H, Salimi S, Khorashad A S 2020 Opt. Commun. 461 125287
Google Scholar
[14] Tomamichel M, Lim C C W, Gisin N, Renner R 2012 Nat. Commun. 3 634
Google Scholar
[15] Ng N H Y, Berta M, Wehner S 2012 Phys. Rev. A 86 042315
Google Scholar
[16] Ming F, Wang D, Shi W N, Huang A J, Du M M, Sun W Y, Ye L 2018 Quantum Inf. Process. 17 267
Google Scholar
[17] Li L J, Ming F, Shi W N, Ye L, Wang D 2021 Physica E 133 114802
Google Scholar
[18] Wang D, Ming F, Huang A J, Sun W Y, Shi J D, Ye L 2017 Laser Phys. Lett. 14 055205
Google Scholar
[19] Wang D, Ming F, Song X K, Ye L, Chen J L 2020 Eur. Phys. J. C 80 800
Google Scholar
[20] Li L J, Ming F, Song X K, Ye L, Wang D 2021 Eur. Phys. J. C 81 72
Google Scholar
[21] Wang T Y, Wang D 2024 Phys. Lett. B 855 138876
Google Scholar
[22] Wang T Y, Wang D 2014 Phys. Lett. A 499 129364
[23] Wu L, Ye L, Wang D 2022 Phys. Rev. A 106 062219
Google Scholar
[24] Xie B F, Ming F, Wang D, Ye L, Chen J L 2021 Phys. Rev. A 104 062204
Google Scholar
[25] Ming F, Wang D, Fan X G, Shi W N, Ye L, Chen J L 2020 Phys. Rev. A 102 012206
Google Scholar
[26] Bouafia Z, Oumennana M, Mansour M, Ouchni F 2024 Appl. Phys. B 130 94
[27] Abdel-Wahab N H, Ibrahim T A S, Amin M E, Salah A 2024 Eur. Phys. J. D 78 28
Google Scholar
[28] Macchiavello C, Palma G M 2002 Phys. Rev. A 65 050301
Google Scholar
[29] D′Arrigo A, Benenti G, Falci G 2007 New. J. Phys. 9 310
Google Scholar
[30] D′Arrigo A, Benenti G, Falci G 2013 Phys. Rev. A 88 042337
Google Scholar
[31] Sk R, Panigrehi P K 2024 Phys. Rev. A 109 032425
Google Scholar
[32] Guo Y N, Fang M F, Wang G Y, Zeng K 2016 Quantum Inf. Process. 15 5129
Google Scholar
[33] Peng Z Y, Wu F L, Li J, Xue H N, Liu S Y, Wang Z Y 2023 Phys. Rev. A 107 022405
Google Scholar
[34] Yu M, Guo Y N 2024 Int. J. Theor. Phys 63 156
Google Scholar
[35] Xie Y X, Qin Z Y 2020 Quantum Inf. Process. 19 375
Google Scholar
[36] 董曜, 纪爱玲, 张国锋 2022 物理学报 71 070303
Google Scholar
Dong Yao, Ji A L, Zhang G F 2022 Acta Phys. Sin. 71 070303
Google Scholar
[37] Zhang D H, Wu F L, Peng Z Y, Wang L, Liu S Y 2023 Quantum Inf. Process. 22 102
Google Scholar
[38] Xu K, Zhang G F, Liu W M 2019 Phys. Rev. A 100 052305
Google Scholar
[39] Haseli S, Hadipour M 2022 Int. J. Theor. Phys 61 117
Google Scholar
[40] Awasthi N, Joshi D K, Sachdev S 2022 Int. J. Theor. Phys 61 123
Google Scholar
[41] Hou L, Zhang Y N, Zhu Y G 2024 Int. J. Theor. Phys 62 221
[42] Lindblad G 1976 Comm. Math. Phys 48 119
Google Scholar
[43] Wolf M M, Eisert J, Cubitt T S, Cirac J I 2008 Phys. Rev. Lett. 101 150402
Google Scholar
[44] Lambert N, Chen Y N, Cheng Y C, Li C M, Chen G Y, Nori F 2013 Nat. Phys. 9 10
Google Scholar
[45] Hwang B, Goan H S 2012 Phys. Rev. A 85 032321
Google Scholar
[46] Banu H, Rao K R 2024 Eur. Phys. J. Plus 139 436
Google Scholar
[47] Addis C, Karpat G, Macchiavello C, Maniscalco 2016 Phys. Rev. A 94 032121
Google Scholar
[48] AWasthi N, Haseli S, Johri U C, Salimi S, Dolatkhah H 2020 Quantum Inf. Process. 19 10
Google Scholar
[49] Wang G Y, Guo Y N, Zeng K 2018 Journal of Modern Optics 66 367
[50] 李丽娟, 明飞, 宋学科, 叶柳, 王栋 2022 物理学报 71 070302
Google Scholar
Li L J, Ming F, Song X K, Liu Y, Wang Dong 2022 Acta Phys. Sin. 71 070302
Google Scholar
[51] Hajihoseinlou H, Ahansaz B 2024 Laser Phys. 34 075202
Google Scholar
[52] Daffer S, Wodkiewicz K, Cresser J D, McIver J K 2004 Phys. Rev. A 70 010304(R
Google Scholar
[53] Cai X 2020 Sci. Rep. 10 88
Google Scholar
[54] Breuer H P, Laine E M, Piilo J 2009 Phys. Rev. Lett. 103 210401
Google Scholar
[55] Chen M N, Wang D, Ye L 2019 Phys. Lett. A 383 977
Google Scholar
[56] Wang D, Huang A J, Hoehn R D, Ming F, Sun W Y, Shi J Dong, Ye L, Kais S 2017 Sci. Rep. 7 1066
Google Scholar
[57] Xu Z Y, Yang W L, Feng M 2012 Phys. Rev. A 86 012113
Google Scholar
[58] Hu M L, Zhou W 2019 Laser Phys. Lett. 16 045201
Google Scholar
[59] Hu M L, Fan H 2020 Sci. China-Phys. Mech. Astron 63 230322
Google Scholar
[60] Hu M L, Zhang Y H, Fan H 2021 Chin. Phys. B 30 030308
Google Scholar
[61] Wootters W K 1998 Phys. Rev. Lett. 80 2245
Google Scholar
[62] Ollivier H, Zurek W H 2001 Phys. Rev. Lett. 88 017901
Google Scholar
[63] Mazzola L, Piilo J, Maniscalco S 2011 Int. J. Quantum Inf. 09 981
Google Scholar
[64] Pati A K, Wilde M M, Devi A R U, Rajagopal A K, Sudha 2012 Phys. Rev. A 86 042105
Google Scholar
[65] Hu M L, Fan H 2013 Phys. Rev. A 88 014105
Google Scholar
[66] Hu M L, Fan H 2013 Phys. Rev. A 87 022314
Google Scholar
DownLoad:
Metrics
- Abstract views: 259
- PDF Downloads: 10
- Cited By: 0
