Quantum Markov monogamy inequalities

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.

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• Quantum processes as thermodynamic resources: the role of non-Markovianity
• Hidden Quantum Memory: Is Memory There When Somebody Looks?
• Relations between Markovian and non-Markovian correlations in multitime quantum processes
• Classical and quantum parts of conditional mutual information for open quantum systems
• Process tensor distinguishability measures
• Efficient and operational quantifier of non-divisibility in terms of channel discrimination