Monogamy of temporal correlations: Witnessing non-Markovianity beyond data processing
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...
| Authors: | , , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2020 |
| Country: | Brasil |
| Institution: | Universidade Federal do Rio Grande do Norte (UFRN) |
| Repository: | Repositório Institucional da UFRN |
| Language: | English |
| OAI Identifier: | oai:repositorio.ufrn.br:123456789/30094 |
| Online Access: | https://repositorio.ufrn.br/jspui/handle/123456789/30094 |
| Access Level: | Open access |
| Keyword: | Quantum Channels Quantum correlations in quantum information Quantum measurements Non-Markovian processes |
| Summary: | 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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