Operational Markov condition for quantum processes

Abstract

We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations, such as the size of the memory required to simulate a process, or the experimental falsifiability of a Markovian hypothesis.

5+3 pages, 4 figures; split off from earlier version of arXiv:1512.00589

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• Thermodynamics of Quantum Causal Models: An Inclusive, Hamiltonian Approach
• Quantum Markovianity as a supervised learning task
• Entropic and trace distance based measures of non-Markovianity
• Quantum regression in dephasing phenomena
• Quantum Memristors in Frequency-Entangled Optical Fields
• Non-Markovianity, information backflow and system-environment correlation for open-quantum-system processes
• Quantum non-Markovian environment-to-system backflows of information: non-operational vs. operational approaches
• Multipartite correlations in quantum collision models
• Correlations, information backflow, and objectivity in a class of pure dephasing models
• Detection of Bidirectional System-Environment Information Exchanges
• A solvable class of non-Markovian quantum multipartite dynamics
• Quantify the Non-Markovian Process with Intervening Projections in a Superconducting Processor
• Memory effects in quantum dynamics modelled by quantum renewal processes
• Detecting Non-Markovianity via Linear Entropy of Choi State
• Equilibration and Typicality in Quantum Processes
• George Sudarshan and Quantum Dynamics