Abstract
The information encoded into an open quantum system that evolves under a Markovian dynamics is always monotonically non-increasing. Nonetheless, for a given quantifier of the information contained in the system, it is in general not clear if for all non-Markovian dynamics it is possible to observe a non-monotonic evolution of this quantity, namely a backflow. We address this problem by considering correlations of finite-dimensional bipartite systems. For this purpose, we consider a class of correlation measures and prove that if the dynamics is non-Markovian there exists at least one element from this class that provides a correlation backflow. Moreover, we provide a set of initial probe states that accomplish this witnessing task. This result provides the first one-to-one relation between non-Markovian quantum dynamics and correlation backflows. Finally, we introduce a measure of non-Markovianity.
Highlights
The information encoded into an open quantum system that evolves under a Markovian dynamics is always monotonically non-increasing
A framework based on a notion of divisibility of dynamical maps, namely the operators describing the dynamical evolution of the system, achieved a promising consensus [2,3,4,5,6,7,8,9,10]
The main result of this work is the first proof of a one-to-one relation between correlation backflows and nonMarkovian dynamics
Summary
In order to prove this, we apply a general POVM {PA,i}i both on ρAB and ρAB and we show that the respective output ensembles are defined by the same probability distribution. The output ensemble that we obtain applying a generic P-POVM {PA,i}i on A for ρ(AλB) (t) different from {|i i|A}i is. Since Pg(ρ(A1B) (τ), {|i i|A}i) = 1, an optimal P-POVM different from {|i i|A}i must provide an output ensemble E(ρ(A1B) (τ), {PA,i}i) of orthogonal states. Let us consider a distance measure d(·, ·) on B(HA) and define a sequence O(δi) of semi-open sets as the P-POVMs {PA,i}i such that d(PA,i, |i i|A) < δi for any i = 1, ..., n, for a strictly decreasing sequence δi+1 < δi where δi → 0 as i → ∞.
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