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arXiv · 1710.06771

Divisibility and Information Flow Notions of Quantum Markovianity for Noninvertible Dynamical Maps

Dariusz Chruściński·Ángel Rivas·Erling Størmer
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Abstract

We analyze the relation between CP-divisibility and the lack of information backflow for an arbitrary -- not necessarily invertible -- dynamical map. It is well known that CP-divisibility always implies lack of information backflow. Moreover, these two notions are equivalent for invertible maps. In this letter it is shown that for a map which is not invertible the lack of information backflow always implies the existence of completely positive (CP) propagator which, however, needs not be trace-preserving. Interestingly, for a {\em wide class of image non-increasing dynamical maps} this propagator becomes trace-preserving as well and hence the lack of information backflow implies CP-divisibility. This result sheds new light into the structure of the time-local generators giving rise to CP-divisible evolutions. We show that if the map is not invertible then positivity of dissipation/decoherence rates is no longer necessary for {CP-}divisibility.

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Dariusz Chruściński, Ángel Rivas, Erling Størmer. 2018-08-28. Divisibility and Information Flow Notions of Quantum Markovianity for Noninvertible Dynamical Maps. https://doi.org/10.1103/physrevlett.121.080407

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