Please wait a minute...
Chin. Phys. B, 2024, Vol. 33(6): 060303    DOI: 10.1088/1674-1056/ad3810
GENERAL Prev   Next  

Quantum discord and its dynamics for multipartite systems

Jiaxin Luo(罗嘉欣) and Qiong Guo(郭琼)†
College of Sciences, Shanghai Institute of Technology, Shanghai 201418, China
Abstract  Quantum discord, one of the famous quantum correlations, has been recently generalized to multipartite systems by Radhakrishnan et al. Here we give analytical solutions of the quantum discord for a family of $N$-qubit quantum states. For the bipartite system, we derive a zero quantum discord which will remain unchanged under the phase damping channel. For multiparitite systems, it is found that the quantum discord can be classified into three categories and the quantum discord for odd-partite systems can exhibit freezing under the phase damping channel, while the freezing does not exist in the even-partite systems.
Keywords:  quantum discord      multipartite systems      decoherence channels      frozen discord  
Received:  19 February 2024      Revised:  14 March 2024      Accepted manuscript online:  27 March 2024
PACS:  03.65.Aa (Quantum systems with finite Hilbert space)  
  03.67.-a (Quantum information)  
  03.65.Yz (Decoherence; open systems; quantum statistical methods)  
Fund: This work was partially supported by the National Natural Science Foundation of China (Grant No. 11601338).
Corresponding Authors:  Qiong Guo     E-mail:  qiongguo@sit.edu.cn

Cite this article: 

Jiaxin Luo(罗嘉欣) and Qiong Guo(郭琼) Quantum discord and its dynamics for multipartite systems 2024 Chin. Phys. B 33 060303

[1] Ollivier H and Zurek W H 2001 Phys. Rev. Lett. 88 017901
[2] Henderson L and Vedral V 2001 J. Phys. A: Math. Gen. 34 6899
[3] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[4] Pirandola S 2014 Sci. Rep. 4 6954
[5] Dakić B, Lipp Y O, Ma X, Ringbauer M, Kropatschek S, Barz S, Paterek T, Vedral V, Zeilinger A, Brukner Č and Walther P 2012 Nat. Phys. 8 666
[6] Chuan T K, Maillard J, Modi K, Paterek T, Paternostro M and Piani M 2012 Phys. Rev. Lett. 109 070501
[7] Bera A, Das T, Sadhukhan D, Roy S S, Sen(De) A and Sen U 2018 Rep. Prog. Phys. 81 024001
[8] Shabani A and Lidar D A 2009 Phys. Rev. Lett. 102 100402
[9] Dakić B, Vedral V and Brukner Č 2010 Phys. Rev. Lett. 105 190502
[10] Huang J H, Wang L and Zhu S Y 2011 New. J. Phys. 13 063045
[11] Bylicka B and Chruściński D 2012 Open Syst. Inf. Dyn. 19 1250006
[12] Akhtarshenas S J, Mohammadi H, Karimi S and Azmi Z 2015 Quantum Inf. Proc. 14 247
[13] Dutta S, Adhikari B and Banerjee S 2017 Quantum Inf. Proc. 16 183
[14] Modi K, Paterek T, Son W, Vedral V and Williamson M 2010 Phys. Rev. Lett. 104 080501
[15] Rulli C C and Sarandy M S 2011 Phys. Rev. A 84 042109
[16] Okrasa M and Walczak Z 2011 Euro. Phys. Lett. 96 60003
[17] Giorgi G L, Bellomo B, Galve F and Zambrini R 2011 Phys. Rev. Lett. 107 190501
[18] Chakrabarty I, Agrawal P and Pati A K 2011 Eur. Phys. J. D 65 605
[19] Radhakrishnan C, Laurière M and Byrnes T 2020 Phys. Rev. Lett. 124 110401
[20] Luo S L 2008 Phys. Rev. A 77 042303
[21] Ali M, Rau A R P and Alber G 2010 Phys. Rev. A 81 042105
[22] Lang M D and Caves C M 2010 Phys. Rev. Lett. 105 150501
[23] Li B, Wang Z X and Fei S M 2011 Phys. Rev. A 83 022321
[24] Shi M J, Sun C X, Jiang F J, Yan X H and Du J F 2012 Phys. Rev. A 85 064104
[25] Maldonado-Trapp A, Hu A and Roa L 2015 Quantum Inf. Proc. 14 1947
[26] Xiao Y L, Li T, Fei S M, Jing N H, Wang Z X and Li-Jost X Q 2016 Chin. Phys. B 25 030301
[27] Jing N H and Yu B 2016 J. Phys. A: Math. Theor. 49 385302
[28] Zhu X N, Fei S M and Li-Jost X 2018 Quantum Inf. Proc. 17 234
[29] Xie C M, Zhang Z J, Chen J L and Yin X F 2020 Entropy 22 147
[30] Zhou J M, Hu X L and Jing N H 2020 Int. J. Theor. Phys. 59 415
[31] Vinjanampathy S and Rau A R P 2012 J. Phys. A: Math. Theor. 45 095303
[32] Rau A R P 2018 Quantum Inf. Proc. 17 216
[33] Ma Z H, Chen Z H, Fanchini F F and Fei S M 2015 Sci. Rep. 5 10262
[34] Yurischev M A 2015 Quantum Inf. Proc. 14 3399
[35] Wu X and Zhou T 2015 Quantum Inf. Proc. 14 1959
[36] Akhtarshenas S J, Mohammadi H, Mousavi F S and Nassajpour V 2015 Int. J. Theor. Phys. 54 72
[37] Piani M 2016 Phys. Rev. Lett. 117 080401
[38] Zhang Q H, Wang J, Shen S Q and Li M 2016 Int. J. Theor. Phys. 55 2148
[39] Huang J W, Xu W and Zheng Z J 2022 Int. J. Theor. Phys. 61 68
[40] Beggi A, Buscemi F and Bordone P 2015 Quantum Inf. Proc. 14 573
[41] Ramkarthik M S, Tiwari D and Barkataki P 2020 Int. J. Theor. Phys. 59 4040
[42] Zhu C L, Hu B, Li B, Wang Z X and Fei S M 2022 Quantum Inf. Proc. 21 264
[43] Zhou X and Zheng Z J 2022 Eur. Phys. J. Plus 137 625
[44] Xiong C H, Qi W T, Miao M K and Wu M H 2023 Chin. Phys. B 32 100301
[45] Li B, Zhu C L, Liang X B, Ye B L and Fei S M 2021 Phys. Rev. A 104 012428
[46] Zhou J M, Hu X L and Jing N H 2022 Quantum Inf. Proc. 21 147
[47] Huang Z M, Qiu D W and Mateus P 2016 Quantum Inf. Proc. 15 301
[48] Jing N H and Yu B 2017 Quantum Inf. Proc. 16 99
[49] Espoukeh P, Rahimi R, Salimi S and Pedram P 2015 Int. J. Quantum Inf. 13 1550044
[50] Hou X W 2023 Physica A 620 128742
[51] Werlang T, Souza S, Fanchini F F and Villas-Bôas C J 2009 Phys. Rev. A 80 024103
[52] Mazzola L, Piilo J and Maniscalco S 2010 Phys. Rev. Lett. 104 200401
[53] Hou J X, Liu S Y, Wang X H and Yang W L 2017 Phys. Rev. A 96 042324
[54] Ban M 2019 Phys. Rev. A 99 012116
[55] Nielsen M and Chuang I 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) p. 383
[1] Geometric discord of tripartite quantum systems
Chunhe Xiong(熊春河), Wentao Qi(齐文韬), Maoke Miao(缪茂可), and Minghui Wu(吴明晖). Chin. Phys. B, 2023, 32(10): 100301.
[2] Protecting geometric quantum discord via partially collapsing measurements of two qubits in multiple bosonic reservoirs
Xue-Yun Bai(白雪云) and Su-Ying Zhang(张素英). Chin. Phys. B, 2022, 31(4): 040308.
[3] Controlling the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environments
Rong-Yu Wu(伍容玉) and Mao-Fa Fang(方卯发). Chin. Phys. B, 2021, 30(3): 037302.
[4] Geometrical quantum discord and negativity of two separable and mixed qubits
Tang-Kun Liu(刘堂昆), Fei Liu(刘飞), Chuan-Jia Shan(单传家), Ji-Bing Liu(刘继兵). Chin. Phys. B, 2019, 28(9): 090304.
[5] Quantum discord of two-qutrit system under quantum-jump-based feedback control
Chang Wang(王畅), Mao-Fa Fang(方卯发). Chin. Phys. B, 2019, 28(12): 120302.
[6] Decoherence for a two-qubit system in a spin-chain environment
Yang Yang(杨阳), An-Min Wang(王安民), Lian-Zhen Cao(曹连振), Jia-Qiang Zhao(赵加强), Huai-Xin Lu(逯怀新). Chin. Phys. B, 2018, 27(9): 090302.
[7] Thermal quantum correlations of a spin-1/2 Ising-Heisenberg diamond chain with Dzyaloshinskii-Moriya interaction
Yidan Zheng(郑一丹), Zhu Mao(毛竹), Bin Zhou(周斌). Chin. Phys. B, 2018, 27(9): 090306.
[8] Comparative investigation of freezing phenomena for quantum coherence and correlations
Lian-Wu Yang(杨连武), Wei Han(韩伟), Yun-Jie Xia(夏云杰). Chin. Phys. B, 2018, 27(4): 040302.
[9] Some studies of the interaction between two two-level atoms and SU(1, 1) quantum systems
T M El-Shahat, M Kh Ismail. Chin. Phys. B, 2018, 27(10): 100201.
[10] Geometric global quantum discord of two-qubit states
Yunlong Xiao(肖运龙), Tao Li(李陶), Shao-Ming Fei(费少明), Naihuan Jing(景乃桓), Zhi-Xi Wang(王志玺), Xianqing Li-Jost(李先清). Chin. Phys. B, 2016, 25(3): 030301.
[11] Phase effect on dynamics of quantum discord modulated by interaction between qubits
Wang Guo-You (王国友), Guo You-Neng (郭有能), Zeng Hao-Sheng (曾浩生). Chin. Phys. B, 2015, 24(9): 090303.
[12] Quantum correlation dynamics in a two-qubit Heisenberg XYZ model with decoherence
Yang Guo-Hui (杨国晖), Zhang Bing-Bing (张冰冰), Li Lei (李磊). Chin. Phys. B, 2015, 24(6): 060302.
[13] Dynamics of super-quantum discord and direct control with weak measurement in open quantum system
Ji Ying-Hua (嵇英华). Chin. Phys. B, 2015, 24(12): 120302.
[14] Characterizing the dynamics of quantum discord under phase damping with POVM measurements
Jiang Feng-Jian (蒋峰建), Ye Jian-Feng (叶剑锋), Yan Xin-Hu (闫新虎), Lü Hai-Jiang (吕海江). Chin. Phys. B, 2015, 24(10): 100304.
[15] Symmetric quantum discord for a two-qubit state
Wang Zhong-Xiao (王仲宵), Wang Bo-Bo (王波波). Chin. Phys. B, 2014, 23(7): 070305.
No Suggested Reading articles found!