General optimality of the Heisenberg limit for quantum metrology

TL;DR

This paper provides a comprehensive proof that the Heisenberg limit represents the ultimate sensitivity bound in quantum metrology, reconciling physical resource definitions with information-theoretic principles.

Contribution

It offers a general optimality proof of the Heisenberg limit by connecting physical resource measures with information-theoretic query complexity.

Findings

Heisenberg limit is the ultimate sensitivity bound in quantum metrology

Resolves paradoxes suggesting sensitivities beyond the Heisenberg limit

Links the Heisenberg limit to the Margolus-Levitin bound, not Heisenberg's uncertainty

Abstract

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.