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The information loss of a stochastic map

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arxiv 2107.01975 v3 pith:5FI76PQR submitted 2021-07-05 cs.IT math.CTmath.ITmath.PR

James Fullwood , Arthur J. Parzygnat This is my paper · ORCID
classification cs.ITmath.CTmath.ITmath.PR
keywords informationconditionallosscharacterizationentropyintroducemeasuresrule
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We provide a stochastic extension of the Baez-Fritz-Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the conditional entropy and a closely related information-theoretic measure that we call conditional information loss. Although not functorial, these information measures are semi-functorial, a concept we introduce that is definable in any Markov category. We also introduce the notion of an entropic Bayes' rule for information measures, and we provide a characterization of conditional entropy in terms of this rule.

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  1. Quantum information loss

    quant-ph 2026-08 conditional novelty 6.0 of 10

    A new quantum information loss measure, minimized over input ensembles and output measurements, vanishes exactly when a code satisfies the Knill-Laflamme error-correction conditions.

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