Quantum Markov monogamy inequalities

TL;DR

This paper introduces quantum Markov monogamy inequalities, a new class of necessary conditions for quantum Markov processes, linking classical and quantum Markovianity and demonstrating their strength over traditional data processing inequalities.

Contribution

The paper develops quantum Markov monogamy inequalities inspired by classical counterparts, providing stronger constraints on quantum Markov processes using the process tensor formalism.

Findings

Quantum Markov monogamy inequalities are introduced as necessary conditions.

These inequalities can be stronger than standard quantum data processing inequalities.

A family of multitime inequalities based on the process tensor formalism is constructed.

Abstract

Markovianity lies at the heart of communication problems. This in turn makes the information-theoretic characterization of Markov processes worthwhile. Data processing inequalities are ubiquitous in this sense, assigning necessary conditions for all Markov processes. We address here the problem of the information-theoretic analysis of constraints on Markov processes in the quantum regime. We show the existence of a novel class of quantum data processing inequalities called here quantum Markov monogamy inequalities. This new class of necessary conditions on quantum Markov processes is inspired by its counterpart for classical Markov processes, and thus providing a strong link between classical and quantum constraints on Markovianity. We go on to construct a family of multitime quantum Markov monogamy inequalities, based on the process tensor formalism and that exploits multitime correlations. We then show, by means of an explicit example, that the Markov monogamy inequalities can be stronger than the usual quantum data processing inequalities.