JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (2): 28-33.doi: 10.6040/j.issn.1671-9352.0.2020.423

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Some characterizations of Markov quantum states

LYU Xiao-le, CHEN Zheng-li*, NIU Meng-fei   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Published:2021-01-21

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Abstract: By using operator theory and matrix theory, the significance of studying Markov quantum states is given. According to the definition of Markov quantum states and the related properties of von Neumann entropy, two necessary and sufficient conditions for a pure state to be a Markov quantum state and two sufficient conditions for a mixed state to be a Markov quantum state are proved.

Key words: Markov state, density matrix, von Neumann entropy

CLC Number: 

  • O177.1
[1] HAYDEN P, JOZSA R, PETZ D, et al. Structure of states which satisfy strong subadditivity of quantum entropy with equality[J]. Communications in Mathematical Physics, 2004, 246(2):359-374.
[2] SARGOLZAHI I. Reference state for arbitrary U-consistent subspace[J]. Journal of Physics A: Mathematical and Theoretical, 2018, 51(31):315301.
[3] BUSCEMI F. Complete positivity, Markovianity, and the quantum data-processing inequality, in the presence of initial system-environment correlations[J]. Physical Review Letters, 2014, 113(14):140502.
[4] LU X M. Structure of correlated initial states that guarantee completely positive reduced dynamics[J]. Physical Review A, 2016, 93(4):042332.
[5] JOSEPH L, SHAJI A. Reference system and not completely positive open quantum dynamics[J]. Physical Review A, 2018, 97(3):032127.
[6] BRODUTCH A, DATTA A, MODI K, et al. Vanishing quantum discord is not necessary for completely positive maps[J]. Physical Review A, 2013, 87(4):252-259.
[7] RODRÍGUEZ-ROSARIO C A, MODI K, KUAH A, et al. Completely positive maps and classical correlations[J]. Journal of Physics A: Mathematical and Theoretical, 2008, 41(20):205301.
[8] NIELSEN M A,CHUANG I L. Quantum computation and quantum information[M]. Cambridge: Cambridge University Press, 2000.
[9] LIEB E H, RUSKAI M B. Proof of the strong subadditivity of quantum-mechanical entropy[J]. Journal of Mathematical Physics, 1973, 14(12):1938-1941.
[10] GUO Zhihua, CAO Huaixin. Local quantum channels preserving quantum correlation[J]. Journal of Physics A: Mathematical and Theoretical, 2013, 46(6):065303.
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