Unidirectional information flow and positive divisibility are nonequivalent notions of quantum Markovianity for noninvertible dynamics

TL;DR

This paper demonstrates that for noninvertible quantum dynamics, the concepts of positive divisibility and information backflow are not equivalent, challenging existing notions of quantum Markovianity.

Contribution

It constructs a specific example of a noninvertible dynamical map that defies the equivalence of two common quantum Markovianity definitions.

Findings

Constructed a nonpositive divisible dynamical map without information backflow

Shows the two quantum Markovianity notions are nonequivalent for noninvertible dynamics

Provides evidence against the equivalence of these definitions in general cases

Abstract

We construct a dynamical map which is not positive divisible and does not present information backflow either (as measured by trace norm quantifiers). It is formulated for a qutrit system undergoing noninvertible dynamics. This provides an evidence that the two definitions of quantum Markovianity based on absence of information backflow and positive divisibility are nonequivalent for general noninvertible dynamical maps