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Title: Conditional uncertainty principle
Authors: Gour, Gilad
Grudka, Andrzej
Horodecki, Michał
Kłobus, Waldemar
Łodyga, Justyna
Narasimhachar, Varun
Keywords: Conditional Uncertainty
Conditional Majorization
Issue Date: 2018
Source: Gour, G., Grudka, A., Horodecki, M., Kłobus, W., Łodyga, J., & Narasimhachar, V. (2018). Conditional uncertainty principle. Physical Review A, 97(4), 042130-.
Series/Report no.: Physical Review A
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.
ISSN: 2469-9926
DOI: 10.1103/PhysRevA.97.042130
Rights: © 2018 American Physical Society. This paper was published in Physical Review A and is made available as an electronic reprint (preprint) with permission of American Physical Society. The published version is available at: []. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.
Fulltext Permission: open
Fulltext Availability: With Fulltext
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