Holevo skew divergence for the characterization of information backflow

Abstract

The interpretation of non-Markovian effects as due to the information exchange between an open quantum system and its environment has been recently formulated in terms of properly regularized entropic quantities, as their revivals in time can be upper bounded by means of quantities describing the storage of information outside the open system [Phys. Rev. Lett. 127, 030401 (2021)]. Here, we elaborate on the wider mathematical framework of the theory, specifying the key properties that allow us to associate distinguishability quantifiers with the information flow from and towards the open system. We point to the Holevo quantity as a distinguished quantum divergence to which the formalism can be applied, and we show how several distinct quantifiers of non-Markovianity can be related to each other within this general framework. Finally, we apply our analysis to two relevant physical models in which an exact evaluation of all quantities can be performed.

10+1 pages, 1 figure; v2: closer to the published version

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Cited by in corpus (11)

• Entropic and trace distance based measures of non-Markovianity
• Correlations, information backflow, and objectivity in a class of pure dephasing models
• Quantum versus classical $P$-divisibility
• Comparison of Distances and Entropic Distinguishability Quantifiers for the Detection of Memory Effects
• Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
• Memory effects in multipartite systems coupled by non-diagonal dephasing mechanisms
• Non-Markovianity in the Adapted Caldeira-Leggett model
• Nonequilibrium quantum thermometry with noncommutative system-bath couplings
• Phase space measures of information flow in open systems: A quantum and classical perspective of non-Markovianity
• Divisibility of dynamical maps: Schrödinger vs. Heisenberg picture
• Superactivation of memory effects in a classical Markov environment