Monogamy of Temporal Correlations: Witnessing non-Markovianity Beyond Data Processing

TL;DR

This paper introduces monogamy-like constraints that characterize Markovian processes and links causality quantification to violations of these constraints, providing new tools to detect non-Markovianity in classical and quantum systems.

Contribution

It establishes the existence of monogamy-like constraints beyond data processing inequalities for Markov chains and connects causality measures to violations of these constraints.

Findings

Monogamy-like constraints are respected by Markov chains.

Violations of these constraints indicate non-Markovianity.

Applicable to quantum measurements for witnessing non-Markovian effects.

Abstract

The modeling of natural phenomena via a Markov process --- a process for which the future is independent of the past, given the present--- is ubiquitous in many fields of science. Within this context, it is of foremost importance to develop ways to check from the available empirical data if the underlying mechanism is indeed Markovian. A paradigmatic example is given by data processing inequalities, the violation of which is an unambiguous proof of the non-Markovianity of the process. Here, our aim is twofold. First we show the existence of a monogamy-like type of constraints, beyond data processing, respected by Markov chains. Second, to show a novel connection between the quantification of causality and the violation of both data processing and monogamy inequalities. Apart from its foundational relevance in the study of stochastic processes we also consider the applicability of our results in a typical quantum information setup, showing it can be useful to witness the non-Markovianity arising in a sequence of quantum non-projective measurements.