General Optimality of the Heisenberg Limit for Quantum Metrology

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Zwierz, Marcin
A. Pe´rez-Delgado, Carlos
Kok, Pieter
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2010
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Abstract

Quantum metrology promises improved sensitivity in parameter estimation over classical procedures. However, there is a debate over the question of how the sensitivity scales with the resources and the number of queries that are used in estimation procedures. Here, we reconcile the physical definition of the relevant resources used in parameter estimation with the information-theoretical scaling in terms of the query complexity of a quantum network. This leads to a completely general optimality proof of the Heisenberg limit for quantum metrology. We give an example of how our proof resolves paradoxes that suggest sensitivities beyond the Heisenberg limit, and we show that the Heisenberg limit is an information-theoretic interpretation of the Margolus-Levitin bound, rather than Heisenberg's uncertainty relation.

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Physical Review Letters

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105

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18

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© 2010 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.

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Quantum Information, Computation and Communication

Quantum Optics

Quantum Physics not elsewhere classified

Mathematical Sciences

Physical Sciences

Engineering

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