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تسجيل مستخدم جديدMonogamy of Temporal Correlations: Witnessing non-Markovianity Beyond Data Processing
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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 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.
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Markovianity lies at the heart of classical communication problems. This in turn makes the information-theoretic characterization of Markovian processes worthwhile. Data processing inequalities are ubiquitous in this sense, assigning necessary condit
ions for all Markovian processes. We address here the problem of the information-theoretic analysis of constraints on Markovian processes in the quantum regime. Firstly, 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 Markovian processes is inspired by its counterpart for classical Markovian processes, and thus providing a strong link between classical and quantum constraints on Markovianity. Secondly, we show the relevance of such inequalities by considering an example of non-Markovian behaviour witnessed by a monogamy inequality, nevertheless, do not violating any of the remaining data processing inequalities. Lastly, we show how this inequalities can be used to witness non-Markovianity at the level of the process tensor formalism.
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Einstein-Podolsky-Rosen (EPR) steering is a type of quantum correlation which allows one to remotely prepare, or steer, the state of a distant quantum system. While EPR steering can be thought of as a purely spatial correlation there does exist a tem
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