Controlling the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environments

doi:10.1088/1674-1056/abc54d

Abstract The uncertainty principle is a crucial aspect of quantum mechanics. It has been shown that the uncertainty principle can be tightened by quantum discord and classical correlation in the presence of quantum memory. We investigate the control of the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environment. Our results show that the entropic uncertainty of an observed system can be reduced and the quantum discord between the observed system and the quantum memory system can be enhanced in the steady state of the system by adding an dissipative ancilla. Particularly, via preparing the state of the system to the highest excited state with hight fidelity, the entropic uncertainty can be reduced markedly and the quantum discord can be enhanced obviously. We explain these results using the definition of state fidelity. Furthermore, we present an effective strategy to further reduce the the entropic uncertainty and to enhance the the quantum discord via quantum-jump-based feedback control. Therefore, our results may be of importance in the context of quantum information technologies.

Keywords: entropic uncertainty quantum discord dissipative environment ancilla

Received: 03 September 2020
Revised: 08 October 2020
Accepted manuscript online: 28 October 2020

PACS:	73.63.Nm	(Quantum wires)
	03.67.Hk	(Quantum communication)
	03.65.Ud	(Entanglement and quantum nonlocality)
	85.35.Be	(Quantum well devices (quantum dots, quantum wires, etc.))

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12064012 and 11374096).

Corresponding Authors: ^†Corresponding author. E-mail: mffang@hunnu.edu.cn

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Rong-Yu Wu(伍容玉) and Mao-Fa Fang(方卯发) Controlling the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environments 2021 Chin. Phys. B 30 037302

1 Heisenberg W 1927 Z. Phys. 43 172
2 Kennard E H 1927 Z. Phys. 44 326
3 Robertson H P 1929 Phys. Rev. 34 163
4 Maccine L and Pati A K 2014 Phys. Rev. Lett. 113 260401
5 Wang K K, Zhan X, Bian Z H, Li J, Zhang Y S and Xue P 2016 Phys. Rev. A 93 052108
6 Deutsch D 1987 Phys. Rev. Lett. 50 631
7 Kraus K 1987 Phys. Rev. D 35 3070
8 Maassen H and Uffink J 1988 Phys. Rev. Lett. 60 1103
9 Berta M, Christandl M, Colbeck R, Renes J M and Renner R 2010 Nat. Phys. 6 659
10 Renes J and Boileau J 2009 Phys. Rev. Lett. 103 020402
11 Prevedel R, Hamel D R, Colbeck R, Fisher K and Resch K J 2011 Nat. Phys. 7 757
12 Li C F, Xu J S, Xu X Y, Li K and Guo G C 2011 Nat. Phys. 7 752
13 Ollivier H and Zurek W H 2001 Phys. Rev. Lett. 88 017901
14 Henderson L and Vedral V 2001 J. Phys. A 34 6899
15 Werlang T, Souza S, Fanchini F F and Villas Boas C J 2009 Phys. Rev. A 80 024103
16 Wang, B, Xu Z Y, Chen Z A and Feng M 2010 Phys. Rev. A 81 014101
17 Streltsov A, Kampermann H and Bruss D 2011 Phys. Rev. Lett. 106 160401
18 Ciccarello F and Giovannetti V 2012 Phys. Rev. A 85 010102
19 Zhang S Y, Fang M F and Yu M 2016 Int. J. Theor. Phys. 55 1824
20 Steane A M 1996 Phys. Rev. Lett. 77 793
21 Francica F, Plastina F and Maniscalco S 2010 Phys. Rev. A 82 052118
22 Hu M L, Hu X Y, Wang J C, Peng Y, Zhang Y R and Fan H Phys. Rep. 762-764 1
23 Pati A K, Wilde M M, Rajagopal A K and Sudha 2012 Phys. Rev. A 86 042105
24 Hu M L and Fan H 2012 Phys. Rev. A 86 032338
25 Hu M L and Fan H 2013 Phys. Rev. A 87 022314
26 Hu M L and Fan H 2013 Phys. Rev. A 88 014105
27 Zhang J, Liu Y X, Li C W, Tarn T J and Nori F 2009 Phys. Rev. A 79 052308
28 Sauer S, Gneiting C and Buchleitner A 2014 Phys. Rev. A 89 022327
29 Vedral V 2002 Rev. Mod. Phys. 74 197
30 Groisman B, Popescu S and Winter A 2005 Phys. Rev. A 72 032317
31 Ollivier H and Zurek W H 2001 Phys. Rev. Lett. 88 017901
32 Schumacher B and Westmoreland M D 2006 Phys. Rev. A 74 042305
33 Groisman B, Popescu S and Winter A 2005 Phys. Rev. A 72 032317
34 Rulli C C and Sarandy M S 2011 Phys. Rev. A 84 042109
35 Mahdian M, Yousefjani R and Salimi S 2012 Eur. Phys. J. D 66 133
36 Wiseman H M and Milburn G J 2006 Phys. Rev. Lett. 70 548
37 Wiseman H M 1994 Phys. Rev. A 49 2133
38 Hou S C, Huang X L and Yi X X 2010 Phys. Rev. A 82 012336
39 Dewes A, Ong F R, Schmitt V, Lauro R, Boulant N, Bertet P, Vion D and Esteve D 2012 Phys. Rev. Lett. 108 057002
40 Houck A A, Koch J, Devoret M H, Girvin S M and Schoelkopf R J 2009 Quantum Infor. Proc. 8 105
41 Ma S L, Li X K, Liu X Y, Xie J K and Li F L 2019 Phys. Rev. A 99 042336
42 Bouchiat V, Vion D, Joyez P, Esteve D and Devoret M H 1998 Phys. Scr. T 76 165
43 Nakamura Y, Pashkin Y A and Tsai J S 1999 Nauture 398 786

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Controlling the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environments

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