General optimality of the Heisenberg limit for quantum metrology

Details General optimality of the Heisenberg limit for quantum metrology General optimality of the Heisenberg limit for quantum metrology

2010-04-22

arxiv.org/abs/1004.3944v3

Physical Review Letters 105, 180402 (2010)

Physics

Quantum Physics

4 pages, 1 figure. To appear in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.105.180402

Quantum metrology promises improved sensitivity in parameter estimation over classical procedures. However, there is an extensive debate over the question how the sensitivity scales with the resources (such as the average photon number) and 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 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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