Advantage of quantum coherence in postselected metrology

TL;DR

This paper demonstrates that quantum coherence is essential for achieving advantages in postselected metrology, linking coherence to resource costs and validating the theory through optical experiments.

Contribution

It reveals the critical role of quantum coherence in postselected metrology and derives a tradeoff relation between coherence and resource costs, supported by experimental validation.

Findings

Quantum coherence enables advantages in postselected metrology.

A tradeoff relation between coherence and resource costs is established.

Experimental results confirm the theoretical predictions.

Abstract

In conventional measurement, to reach the greatest accuracy of parameter estimation, all samples must be measured since each independent sample contains the same quantum Fisher information. In postselected metrology, postselection can concentrate the quantum Fisher information of the initial samples into a tiny post-selected sub-ensemble. It has been proven that this quantum advantage can not be realized in any classically commuting theory. In this work, we present that the advantage of postselection in weak value amplification (WVA) can not be achieved without quantum coherence. The quantum coherence of the initial system is closely related to the preparation costs and measurement costs in parameter estimation. With the increase of initial quantum coherence, the joint values of preparation costs and measurement costs can be optimized to smaller. Moreover, we derive an analytical tradeoff relation between the preparation, measurement and the quantum coherence. We further experimentally test the tradeoff relation in a linear optical setup. The experimental and theoretical results are in good agreement and show that the quantum coherence plays a key role in bounding the resource costs in the postselected metrology process.