Quantifying non-Markovianity via conditional mutual information

Abstract

In this paper, we study measures of quantum non-Markovianity based on the conditional mutual information. We obtain such measures by considering multiple parts of the total environment such that the conditional mutual information can be defined in this multipartite setup. The benefit of this approach is that the conditional mutual information is closely related to recovery maps and Markov chains; we also point out its relations with the change of distinguishability. We study along the way the properties of leaked information which is the conditional mutual information that can be back flowed, and we use this leaked information to show that the correlated environment is necessary for nonlocal memory effect.

arXiv comment10 pages, 3 figures

References in corpus (25)

• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Non-Markovian dynamics in open quantum systems
• Quantum Resource Theories
• The Role of Relative Entropy in Quantum Information Theory
• Entanglement and non-Markovianity of quantum evolutions
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• "Squashed Entanglement" - An Additive Entanglement Measure
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Operational Markov condition for quantum processes
• On measures of non-Markovianity: divisibility vs. backflow of information
• Geometrical characterization of non-Markovianity
• Quantum conditional mutual information and approximate Markov chains
• Continuity of quantum conditional information
• Foundations and Measures of Quantum Non-Markovianity
• Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information
• Optimal state pairs for non-Markovian quantum dynamics
• Quantifying non-Markovianity of continuous variable Gaussian dynamical maps
• Non-Markovianity through flow of information between a system and an environment
• Fluctuation Theorem for Many-Body Pure Quantum States
• Fidelity of recovery, geometric squashed entanglement, and measurement recoverability
• Almost Markovian processes from closed dynamics
• Competition between memory-keeping and memory-erasing decoherence channels
• Hierarchy of Non-Markovianity and $k$-divisibility phase diagram of Quantum Processes in Open Systems
• Witnessing non-Markovian dynamics through correlations
• Equivalence between non-Markovian dynamics and correlation backflows

Cited by in corpus (10)

• Causal and Non-Causal Revivals of Information: A New Regime of Non-Markovianity in Quantum Stochastic Processes
• Facets of correlated non-Markovian channels
• Multiparty Spohn's theorem for a combination of local Markovian and non-Markovian quantum dynamics
• Transient effects in quantum refrigerators with finite environments
• The impact of memory on learning sequence-to-sequence tasks
• Quantum conditional mutual information of W state in non-inertial frames
• Availing non-Markovian dynamics in effective negative temperature-based transient quantum Otto engines
• Classical and quantum parts of conditional mutual information for open quantum systems
• On the relation between quantum Darwinism and approximate quantum Markovianity
• Ergotropy-Based Quantum Thermodynamics