Parameter estimation with mixed quantum states

TL;DR

This paper proves that in quantum enhanced measurements with mixed states, classical correlations do not improve parameter estimation sensitivity, establishing a fundamental limit based on pure state sensitivities.

Contribution

It provides a general proof that classical correlations cannot enhance sensitivity in quantum measurement schemes involving mixed states.

Findings

Classical correlations do not improve measurement sensitivity.

Sensitivity is bounded by the maximal pure state sensitivity.

The result applies to any linear, smooth dependence on the parameter.

Abstract

We consider quantum enhanced measurements with initially mixed states. We show very generally that for any linear propagation of the initial state that depends smoothly on the parameter to be estimated, the sensitivity is bound by the maximal sensitivity that can be achieved for any of the pure states from which the initial density matrix is mixed. This provides a very general proof that purely classical correlations cannot improve the sensitivity of parameter estimation schemes in quantum enhanced measurement schemes.