Inequivalence of correlation-based measures of non-Markovianity

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Neto, Alaor Cervati [UNESP]
Karpat, Göktuǧ [UNESP]
Fanchini, Felipe Fernandes [UNESP]
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We conclusively show that the entanglement- and the mutual-information-based measures of quantum non-Markovianity are inequivalent. To this aim, we first analytically solve the optimization problem in the definition of the entanglement-based measure for a two-level system. We demonstrate that the optimal initial bipartite state of the open system and the ancillary is always given by one of the Bell states for any one-qubit dynamics. On top of this result, we present an explicit example dynamics where memory effects emerge according to the mutual-information-based measure, even though the time evolution remains memoryless with respect to the entanglement-based measure. Finally, we explain this disagreement between the two measures in terms of the information dynamics of the open system, exploring the accessible and inaccessible parts of information.
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Physical Review A, v. 94, n. 3, 2016.