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Family of generalized "pretty good" measurements and the minimal-error pure-state discrimination problems for which they are optimal

Mochon, Carlos (2006) Family of generalized "pretty good" measurements and the minimal-error pure-state discrimination problems for which they are optimal. Physical Review A, 73 (3). Art. No. 032328. ISSN 1050-2947. https://resolver.caltech.edu/CaltechAUTHORS:MOCpra06

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Abstract

Given a quantum pure state chosen from a set with some a priori probabilities, what is the optimal measurement needed to correctly guess the given state? We show that a good choice is the family of square-root or "pretty good" measurements, as each measurement in the family is optimal for at least one discrimination problem with the same quantum states but possibly different a priori probabilities. Furthermore, the map from measurement to discrimination problems can be explicitly described. In fact, for linearly independent states, every pair of discrimination problem and optimal measurement can be explicitly generated this way.


Item Type:Article
Additional Information:©2006 The American Physical Society. Received 25 December 2005; published 22 March 2006. The author would like to thank Andrew Childs for his help in proofreading this manuscript, and Jon Tyson for his help with some of the bibliography. This work was supported in part by the National Science Foundation under Grant No. EIA-0086038 and by the U.S. Department of Energy under Grant No. DE-FG03-92-ER40701.
Subject Keywords:quantum theory; information theory; error correction; probability
Issue or Number:3
Record Number:CaltechAUTHORS:MOCpra06
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:MOCpra06
Alternative URL:http://dx.doi.org/10.1103/PhysRevA.73.032328
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3842
Collection:CaltechAUTHORS
Deposited By: Lindsay Cleary
Deposited On:14 Jul 2006
Last Modified:02 Oct 2019 23:07

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