Error-tradeoff and error-disturbance relations for incompatible quantum measurements

Branciard, Cyril (2013) Error-tradeoff and error-disturbance relations for incompatible quantum measurements. Proceedings of the National Academy of Sciences of the United States of America, 110 17: 6742-6747. doi:10.1073/pnas.1219331110


Author Branciard, Cyril
Title Error-tradeoff and error-disturbance relations for incompatible quantum measurements
Journal name Proceedings of the National Academy of Sciences of the United States of America   Check publisher's open access policy
ISSN 0027-8424
1091-6490
Publication date 2013-04
Sub-type Article (original research)
DOI 10.1073/pnas.1219331110
Volume 110
Issue 17
Start page 6742
End page 6747
Total pages 6
Place of publication United States
Publisher National Academy of Sciences
Collection year 2014
Language eng
Formatted abstract
Heisenberg’s uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: Although Heisenberg’s first argument was that the measurement of one observable on a quantum state necessarily disturbs another incompatible observable, standard uncertainty relations typically bound the indeterminacy of the outcomes when either one or the other observable is measured. In this paper, we quantify precisely Heisenberg’s intuition. Even if two incompatible observables cannot be measured together, one can still approximate their joint measurement, at the price of introducing some errors with respect to the ideal measurement of each of them. We present a tight relation characterizing the optimal tradeoff between the error on one observable vs. the error on the other. As a particular case, our approach allows us to characterize the disturbance of an observable induced by the approximate measurement of another one; we also derive a stronger error-disturbance relation for this scenario.
Keyword Approximate joint measurements
Error-disturbance tradeoffs
Quantum information
Uncertainty relation
Observables
Principle
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 2014 Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 52 times in Thomson Reuters Web of Science Article | Citations
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