Monogamy of temporal correlations: witnessing non-markovianity beyond data processing
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2020
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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 constraint, beyond data processing, respected by Markov chains. Secondly, we show
a 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 nonprojective measurements.
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CAPELA, Matheus; CÉLERI, Lucas C. ; MODI, Kavan; CHAVES, Rafael. Monogamy of temporal correlations: witnessing non-markovianity beyond data processing. Physical Review Research, Washington, v. 2, n. 1, e013350, 2020. DOI: 10.1103/PhysRevResearch.2.013350. Disponível em: https://arxiv.org/abs/1910.04236. Acesso em: 2 maio 2023.