Continuity bounds on observational entropy and measured relative entropies
Schindler, Joseph (Universitat Autònoma de Barcelona. Departament de Física)
Winter, Andreas (Universitat Autònoma de Barcelona. Departament de Física)

Date:	2023
Abstract:	We derive a measurement-independent asymptotic continuity bound on the observational entropy for general positive operator valued measures measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for other entropic quantities, including the measured relative entropy distance to a convex set of states under a general set of measurements. As a special case, we define and study conditional observational entropy, which is an observational entropy in one (measured) subsystem conditioned on the quantum state in another (unmeasured) subsystem. We also study continuity of relative entropy with respect to a jointly applied channel, finding that observational entropy is uniformly continuous as a function of the measurement. But we show by means of an example that this continuity under measurements cannot have the form of a concrete asymptotic bound.
Grants:	Agencia Estatal de Investigación PCI2022-132965 Agencia Estatal de Investigación PID2019-107609GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1127
Note:	Altres ajuts: acords transformatius de la UAB
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Published in:	Journal of Mathematical Physics, Vol. 64, Issue 9 (September 2023) , art. 92201, ISSN 1089-7658

DOI: 10.1063/5.0147294

14 p, 4.2 MB

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