Concurrence as a measure of Markovianity: concurrence versus distinguishability and divisibility

Gao, Ze-Yu; Ren, Yu-Kun; Zeng, Hao‐Sheng

doi:10.1007/s11128-016-1306-z

Cited by 4 publications

(1 citation statement)

References 32 publications

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“…However, its quantum versions are controversial in some sense [2][3][4][5]. Various non-Markovian criteria have been proposed, and some measures are introduced based on different considerations [6][7][8][9][10][11][12][13][14][15][16], such as the divisibility, mutual information, information distance measures, Fisher information flow, etc. All those non-Markovianity measures do not coincide exactly in general [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Quantifying quantum non-Markovianity based on quantum coherence via skew information

et al. 2019

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Based on the nonincreasing property of quantum coherence via skew information under incoherent completely positive and trace-preserving maps, we propose a non-Markovianity measure for open quantum processes. As applications, by applying the proposed measure to some typical noisy channels, we find that it is equivalent to the three previous measures of non-Markovianity for phase damping and amplitude damping channels, i.e., the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, it is equivalent to the non-Markovianity measure based on l1 norm of coherence for a class of output states and it is incompletely equivalent to the measure based on dynamical divisibility. We also use the modified Tsallis relative α entropy of coherence to detect the non-Markovianity of dynamics of quantum open systems, the results show that the modified Tsallis relative α entropy of coherence are more comfortable than the original Tsallis relative α entropy of coherence for small α. I. INTRODUCTION In recent years, the Markovian and non-Markovian process for open quantum dynamics has attracted much attention. In the classical realm, the Markovian and non-Markovian dynamics are well defined and widely studied [1]. However, its quantum versions are controversial in some sense [2-5]. Various non-Markovian criteria have been proposed, and some measures are introduced based on different considerations [6-16], such as the divisibility, mutual information, information distance measures, Fisher information flow, etc. All those non-Markovianity measures do not coincide exactly in general [17-20]. Finding a universal definition for non-Markovian dynamic is an important subject in quantum information theory.Recently, a rigorous framework of quantifying coherence has been proposed, and several measures of quantum coherence are proposed [21][22][23][24][25][26][27][28], such as the l 1 -norm of coherence, relative entropy of coherence, fidelity of coherence, etc. As is well known, the Kraus operators of the phase damping channels, the amplitude channels and the random unitary channels are qubit incoherent operators, and coherence measures are monotonicity under all the incoherent completely positive and trace-preserving maps. Hence, the coherence measures are employed to investigate the detection of non-Markovianity. Chanda et al. used the l 1 -norm of coherence to define the measure of non-Markovianity, and shew that it is equivalent to the measures based on trace distance, quantum mutual information and quantum *

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Section: Introductionmentioning

confidence: 99%

Quantifying quantum non-Markovianity based on quantum coherence via skew information

et al. 2019

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Non-Markovianity detection with coherence measures based on the Tsallis relativeαentropies

Mirafzali

Baghshahi

2019

Physica A: Statistical Mechanics and its Applications

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Non-Markovianity Measure Based on Brukner–Zeilinger Invariant Information for Unital Quantum Dynamical Maps

He¹,

Zhu²,

Li³

2017

Commun. Theor. Phys.

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A non-Markovianity measure based on Brukner–Zeilinger invariant information to characterize non-Markovian effect of open systems undergoing unital dynamical maps is proposed. The method takes advantage of non-increasing property of the Brukner–Zeilinger invariant information under completely positive and trace-preserving unital maps. The simplicity of computing the Brukner–Zeilinger invariant information is the advantage of the proposed measure because of mainly depending on the purity of quantum state. The measure effectively captures the characteristics of non-Markovianity of unital dynamical maps. As some concrete application, we consider two typical non-Markovian noise channels, i.e., the phase damping channel and the random unitary channel to show the sensitivity of the proposed measure. By investigation, we find that the conditions of detecting the non-Markovianity for the phase damping channel are consistent with the results of existing measures for non-Markovianity, i.e., information flow, divisibility and quantum mutual information. However, for the random unitary channel non-Markovian conditions are same to that of the information flow, but is different from that of the divisibility and quantum mutual information.

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Concurrence as a measure of Markovianity: concurrence versus distinguishability and divisibility

Cited by 4 publications

References 32 publications

Quantifying quantum non-Markovianity based on quantum coherence via skew information

Quantifying quantum non-Markovianity based on quantum coherence via skew information

Non-Markovianity detection with coherence measures based on the Tsallis relativeαentropies

Non-Markovianity Measure Based on Brukner–Zeilinger Invariant Information for Unital Quantum Dynamical Maps

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