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

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.

arXiv comment9 pages + appendix, 2 figures

References in corpus (23)

• Device-independent security of quantum cryptography against collective attacks
• Non-Markovian dynamics in open quantum systems
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (1999)
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Device-independent tests of classical and quantum dimensions
• Operational Markov condition for quantum processes
• Quantum conditional mutual information and approximate Markov chains
• Quantum causal modelling
• Information-Theoretic Implications of Quantum Causal Structures
• Quantifying causal influences
• Polynomial Bell inequalities
• A unifying framework for relaxations of the causal assumptions in Bell's theorem
• Completely Positive Divisibility Does Not Mean Markovianity
• Entropic Inequalities and Marginal Problems
• Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes
• The Structure of Quantum Stochastic Processes with Finite Markov Order
• Device-Independent Tests of Entropy
• Quantifier Elimination for Statistical Problems
• Analysing causal structures with entropy
• Inferring latent structures via information inequalities
• Indistinguishability of causal relations from limited marginals
• Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference

Cited by in corpus (5)

• Quantum stochastic processes and quantum non-Markovian phenomena
• Quantum Memristors in Frequency-Entangled Optical Fields
• Quantum causal correlations and non-Markovianity of quantum evolution
• Quantum Markov monogamy inequalities
• Efficient and operational quantifier of non-divisibility in terms of channel discrimination