Conditional uncertainty principle
Gilad Gour , Andrzej Grudka , Michał Horodecki , Waldemar Kłobus , Justyna Łodyga , Varun Narasimhachar
AbstractWe 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.
|Journal series||Physical Review A, ISSN 1050-2947, (A 35 pkt)|
|Publication size in sheets||0.65|
|Score|| = 35.0, 24-10-2018, ArticleFromJournal|
= 35.0, 24-10-2018, ArticleFromJournal
|Publication indicators||: 2016 = 2.925 (2) - 2016=2.716 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.