Building versatile bipartite probes for quantum metrology

TL;DR

This paper analyzes bipartite quantum states as probes for local transformation estimation, focusing on average performance and resource requirements, with explicit formulas and criteria for optimal probe states based on purity and correlations.

Contribution

It introduces a closed-form computation of average skew information for bipartite states and identifies optimal states for local quantum metrology based on purity and correlations.

Findings

Average skew information depends strongly on local purity.

Explicit criteria for selecting optimal bipartite probes.

Purity and correlations influence the robustness of quantum sensors.

Abstract

We consider bipartite systems as versatile probes for the estimation of transformations acting locally on one of the subsystems. We investigate what resources are required for the probes to offer a guaranteed level of metrological performance, when the latter is averaged over specific sets of local transformations. We quantify such a performance via the average skew information, a convex quantity which we compute in closed form for bipartite states of arbitrary dimensions, and which is shown to be strongly dependent on the degree of local purity of the probes. Our analysis contrasts and complements the recent series of studies focused on the minimum, rather than the average, performance of bipartite probes in local estimation tasks, which was instead determined by quantum correlations other than entanglement. We provide explicit prescriptions to characterize the most reliable states maximizing the average skew information, and elucidate the role of state purity, separability and correlations in the classification of optimal probes. Our results can help in the identification of useful resources for sensing, estimation and discrimination applications when complete knowledge of the interaction mechanism realizing the local transformation is unavailable, and access to pure entangled probes is technologically limited.