Frenkel, Péter Ernő and Weiner, Mihály (2015) Classical Information Storage in an nLevel Quantum System. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 340 (2). pp. 563574. ISSN 00103616

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Abstract
A game is played by a team of two—say Alice and Bob—in which the value of a random variable x is revealed to Alice only, who cannot freely communicate with Bob. Instead, she is given a quantum nlevel system, respectively a classical nstate system, which she can put in possession of Bob in any state she wishes. We evaluate how successfully they managed to store and recover the value of x by requiring Bob to specify a value z and giving a reward of value f (x,z) to the team. We show that whatever the probability distribution of x and the reward function f are, when using a quantum nlevel system, the maximum expected reward obtainable with the best possible team strategy is equal to that obtainable with the use of a classical nstate system. The proof relies on mixed discriminants of positive matrices and—perhaps surprisingly—an application of the Supply–Demand Theorem for bipartite graphs. As a corollary, we get an infinite set of new, dimension dependent inequalities regarding positive operator valued measures and density operators on complex nspace. As a further corollary, we see that the greatest value, with respect to a given distribution of x, of the mutual information I (x; z) that is obtainable using an nlevel quantum system equals the analogous maximum for a classical nstate system. © 2015, SpringerVerlag Berlin Heidelberg.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA71 Number theory / számelmélet Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  17 Feb 2016 10:21 
Last Modified:  17 Feb 2016 10:21 
URI:  http://real.mtak.hu/id/eprint/33623 
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