Generalized formalism for information backflow in assessing Markovianity and its equivalence to divisibility

TL;DR

This paper introduces a comprehensive framework for information backflow in quantum Markovianity, establishing its equivalence to divisibility, and proposes a family of measures to quantify non-Markovianity.

Contribution

It unifies various IB approaches into a single framework, introduces a general 'physicality quantifier', and links IB Markovianity to divisibility and trace-distance criteria.

Findings

Framework encompasses most IB prescriptions

Infinite family of non-Markovianity measures proposed

Trace-distance criterion suffices for IB Markovianity in 2D

Abstract

We present a general framework for the information backflow (IB) approach of Markovianity that not only includes a large number, if not all, of IB prescriptions proposed so far but also is equivalent to completely positive divisibility for invertible evolutions. Following the common approach of IB, where monotonic decay of some physical property or some information quantifier is seen as the definition of Markovianity, we propose in our framework a general description of what should be called a proper `physicality quantifier' to define Markovianity. We elucidate different properties of our framework and use them to argue that an infinite family of non-Markovianity measures can be constructed, which would capture varied strengths of non-Markovianity in the dynamics. Moreover, we show that generalized trace-distance measure in two dimensions serve as a sufficient criteria for IB Markovianity for a number of prescriptions suggested earlier in the literature.