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Title: Base norms and discrimination of generalized quantum channels

Abstract

We introduce and study norms in the space of hermitian matrices, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum states, channels, and networks. We further introduce generalized quantum decision problems and show that the maximal average payoffs of decision procedures are again given by these norms. We also study optimality of decision procedures, in particular, we obtain a necessary and sufficient condition under which an optimal 1-tester for discrimination of quantum channels exists, such that the input state is maximally entangled.

Authors:
 [1]
  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, Bratislava (Slovakia)
Publication Date:
OSTI Identifier:
22251020
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HERMITIAN MATRIX; QUANTUM ENTANGLEMENT; QUANTUM STATES; SPACE

Citation Formats

Jenčová, A. Base norms and discrimination of generalized quantum channels. United States: N. p., 2014. Web. doi:10.1063/1.4863715.
Jenčová, A. Base norms and discrimination of generalized quantum channels. United States. doi:10.1063/1.4863715.
Jenčová, A. Sat . "Base norms and discrimination of generalized quantum channels". United States. doi:10.1063/1.4863715.
@article{osti_22251020,
title = {Base norms and discrimination of generalized quantum channels},
author = {Jenčová, A.},
abstractNote = {We introduce and study norms in the space of hermitian matrices, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum states, channels, and networks. We further introduce generalized quantum decision problems and show that the maximal average payoffs of decision procedures are again given by these norms. We also study optimality of decision procedures, in particular, we obtain a necessary and sufficient condition under which an optimal 1-tester for discrimination of quantum channels exists, such that the input state is maximally entangled.},
doi = {10.1063/1.4863715},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 55,
place = {United States},
year = {Sat Feb 15 00:00:00 EST 2014},
month = {Sat Feb 15 00:00:00 EST 2014}
}
  • We introduce and study norms in the space of hermitian matrices, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum states, channels, and networks. We further introduce generalized quantum decision problems and show that the maximal average payoffs of decision procedures are again given by these norms. We also study optimality of decision procedures, in particular, we obtain a necessary and sufficient condition under which an optimal 1-tester for discrimination of quantum channels exists, such that the input state is maximally entangled.
  • Cited by 1
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  • No abstract prepared.