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Observational entropy, coarse-grained states, and the Petz recovery map: information-theoretic properties and bounds

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Title
Observational entropy, coarse-grained states, and the Petz recovery map: information-theoretic properties and bounds
Author(s)
Buscemi, Francesco; Schindler, Joseph; Dominik Safranek
Publication Date
2023-05
Journal
New Journal of Physics, v.25, no.5
Publisher
Institute of Physics
Abstract
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann’s and Gibbs’ entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic entropy. Here we study the mathematical properties of observational entropy from an information-theoretic viewpoint, making use of recently strengthened forms of the monotonicity property of quantum relative entropy. We present new bounds on observational entropy applying in general, as well as bounds and identities related to sequential and post-processed measurements. A central role in this work is played by what we call the ‘coarse-grained’ state, which emerges from the measurement’s statistics by Bayesian retrodiction, without presuming any knowledge about the ‘true’ underlying state being measured. The degree of distinguishability between such a coarse-grained state and the true (but generally unobservable) one is shown to provide upper and lower bounds on the difference between observational and von Neumann entropies. © 2023 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.
URI
https://pr.ibs.re.kr/handle/8788114/13444
DOI
10.1088/1367-2630/accd11
ISSN
1367-2630
Appears in Collections:
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > 1. Journal Papers (저널논문)
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