Non-Markovianity measure based on the relative entropy of coherence in an extended space

Non-Markovianity measure based on the relative entropy of coherence in an extended space An alternative non-Markovianity measure for open quantum processes is proposed, which takes advantage of the nonincreasing property of relative entropy of coherence under the incoherent completely positive and trace-preserving maps in the extended Hilbert space constituted by the open system and its ancillary. By applying the proposed measure to some typical noisy channels, we find that for phase damping and amplitude damping channels it is equivalent to the three previous measures of non-Markovianity, i.e., the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, however, these measures do not coincide exactly, and the proposed measure in the witness of Markovianity is more general than the measures based on quantum trace distance and dynamical divisibility but overlaps partly with the measure based on quantum mutual information. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Non-Markovianity measure based on the relative entropy of coherence in an extended space

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Non-Markovianity measure based on the relative entropy of coherence in an extended space

Abstract

An alternative non-Markovianity measure for open quantum processes is proposed, which takes advantage of the nonincreasing property of relative entropy of coherence under the incoherent completely positive and trace-preserving maps in the extended Hilbert space constituted by the open system and its ancillary. By applying the proposed measure to some typical noisy channels, we find that for phase damping and amplitude damping channels it is equivalent to the three previous measures of non-Markovianity, i.e., the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, however, these measures do not coincide exactly, and the proposed measure in the witness of Markovianity is more general than the measures based on quantum trace distance and dynamical divisibility but overlaps partly with the measure based on quantum mutual information.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.022106
Publisher site
See Article on Publisher Site

Abstract

An alternative non-Markovianity measure for open quantum processes is proposed, which takes advantage of the nonincreasing property of relative entropy of coherence under the incoherent completely positive and trace-preserving maps in the extended Hilbert space constituted by the open system and its ancillary. By applying the proposed measure to some typical noisy channels, we find that for phase damping and amplitude damping channels it is equivalent to the three previous measures of non-Markovianity, i.e., the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, however, these measures do not coincide exactly, and the proposed measure in the witness of Markovianity is more general than the measures based on quantum trace distance and dynamical divisibility but overlaps partly with the measure based on quantum mutual information.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Aug 4, 2017

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