Conditional uncertainty principle

Gilad Gour , Andrzej Grudka , Michał Horodecki , Waldemar Kłobus , Justyna Łodyga , Varun Narasimhachar

Abstract

We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define conditional majorization and, for the case of classical memory, we provide its thorough characterization in terms of monotones, i.e., functions that preserve the partial order under conditional majorization. We demonstrate the application of this framework by deriving two types of memory-assisted uncertainty relations, (1) a monotone-based conditional uncertainty relation and (2) a universal measure-independent conditional uncertainty relation, both of which set a lower bound on the minimal uncertainty that Bob has about Alice's pair of incompatible measurements, conditioned on arbitrary measurement that Bob makes on his own system. We next compare the obtained relations with their existing entropic counterparts and find that they are at least independent.
Author Gilad Gour
Gilad Gour,,
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, Andrzej Grudka
Andrzej Grudka,,
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, Michał Horodecki (FMPI / ITPA)
Michał Horodecki,,
- Institute of Theoretical Physics and Astrophysics
, Waldemar Kłobus
Waldemar Kłobus,,
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, Justyna Łodyga
Justyna Łodyga,,
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, Varun Narasimhachar
Varun Narasimhachar,,
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Journal seriesPhysical Review A, ISSN 1050-2947, (A 35 pkt)
Issue year2018
Vol97
No4
Pages1-14
Publication size in sheets0.65
DOIDOI:10.1103/PhysRevA.97.042130
URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.042130
Languageen angielski
Score (nominal)35
ScoreMinisterial score = 35.0, 24-10-2018, ArticleFromJournal
Ministerial score (2013-2016) = 35.0, 24-10-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 2.925 (2) - 2016=2.716 (5)
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