Maximally non-Markovian quantum dynamics without environment backflow of information

TL;DR

This paper introduces a class of maximally non-Markovian quantum evolutions where the environment remains Markovian and unaffected by the system, challenging the typical association of non-Markovianity with environment-to-system information backflow.

Contribution

It demonstrates the existence of maximally non-Markovian quantum dynamics with environment dynamics that are Markovian and unperturbed by the system, highlighting a new mechanism for non-Markovianity.

Findings

Environment remains Markovian and unaffected by the system.

Non-Markovian features arise from unidirectional system-reservoir dependence.

Absence of environment-to-system information backflow.

Abstract

The degree of non-Markovianity allows to characterizing quantum evolutions that depart from a Markovian regime in a similar way as Schmidt number measures the degree of entanglement of pure states. Maximally non-Markovian dynamics are the analogous of maximally entangled states [D. Chru\'sci\'nski and S. Maniscalco, Phys. Rev. Lett. 112, 120404 (2014)]. Here, we demonstrate that there exists a class of maximally non-Markovian quantum evolutions where the associated environment (degrees of freedom not belonging to the system) obeys a Markovian (memoryless) dynamics, which in turn is unperturbed by the system state or dynamics. These properties imply the absence of any "physical environment-to-system backflow of information." Non-Markovian features (as usual in quantum systems coupled to dissipative classical degrees of freedom) arise from a unidirectional dependence of the system dynamics on the reservoir states.