Causal and Non-Causal Revivals of Information: A New Regime of Non-Markovianity in Quantum Stochastic Processes

TL;DR

This paper distinguishes between information revivals and backflows in quantum processes, revealing that revivals can occur without backflows and proposing operational criteria to identify genuine non-Markovianity, thereby enabling a convex resource theory.

Contribution

It introduces a clear distinction between revivals and backflows in quantum non-Markovianity and develops criteria to identify genuine backflows, advancing the theoretical framework.

Findings

Revivals can occur without backflows in quantum processes.

Operational conditions to witness genuine backflows are established.

Excluding non-causal revivals makes the resource theory of non-Markovianity convex.

Abstract

The study of information revivals, witnessing the violation of certain data-processing inequalities, has provided an important paradigm in the study of non-Markovian quantum stochastic processes. Although often used interchangeably, we argue here that the notions of ``revivals'' and ``backflows'', i.e., flows of information from the environment back into the system, are distinct: an information revival can occur without any backflow ever taking place. In this paper, we examine in detail the phenomenon of non-causal revivals and relate them to the theory of short Markov chains and squashed non-Markovianity. We also provide an operational condition, in terms of system-only degrees of freedom, to witness the presence of genuine backflow that cannot be explained by non-causal revivals. As a byproduct, we demonstrate that focusing on processes with genuine backflows, while excluding those with only non-causal revivals, resolves the issue of non-convexity of Markovianity, thus enabling the construction of a convex resource theory of genuine quantum non-Markovianity.