Deriving tight error-trade-off relations for approximate joint measurements of incompatible quantum observables

Branciard, Cyril (2014) Deriving tight error-trade-off relations for approximate joint measurements of incompatible quantum observables. Physical Review A, 89 2: 022124.1-022124.16. doi:10.1103/PhysRevA.89.022124

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Author Branciard, Cyril
Title Deriving tight error-trade-off relations for approximate joint measurements of incompatible quantum observables
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
1094-1622
Publication date 2014-02
Year available 2014
Sub-type Article (original research)
DOI 10.1103/PhysRevA.89.022124
Open Access Status File (Publisher version)
Volume 89
Issue 2
Start page 022124.1
End page 022124.16
Total pages 16
Place of publication College Park, United States
Publisher American Physical Society
Collection year 2015
Language eng
Formatted abstract
The quantification of the “measurement uncertainty”aspect of Heisenberg's uncertainty principle—that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two incompatible observables—has regained a lot of interest recently. Several approaches have been proposed and debated. In this paper we consider Ozawa's definitions for inaccuracies (as root-mean-square errors) in approximate joint measurements, and study how these are constrained in different cases, whether one specifies certain properties of the approximations—namely their standard deviations and/or their bias—or not. Extending our previous work [C. Branciard, Proc. Natl. Acad. Sci. USA 110, 6742 (2013)], we derive error-trade-off relations, which we prove to be tight for pure states. We show explicitly how all previously known relations for Ozawa's inaccuracies follow from ours. While our relations are in general not tight for mixed states, we show how these can be strengthened and how tight relations can still be obtained in that case.
Keyword Disturbance Uncertainty Relation
Spin
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 12 times in Thomson Reuters Web of Science Article | Citations
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