Nonclassicality of Mixed States with Photon Number Coherence

TL;DR

This paper develops exact formulas and numerical methods to evaluate the operational resource theory measure of nonclassicality for mixed states with photon number coherence, linking it to metrological power.

Contribution

It provides the first explicit calculations of ORT nonclassicality for mixed states with photon number coherence, including exact formulas for rank-two states and numerical solutions for higher ranks.

Findings

Nonclassicality and metrological power do not increase under bosonic dephasing.

Metrological power can saturate the ORT bound in certain regimes.

Reducing photon number coherence can enhance nonclassicality and metrological usefulness.

Abstract

The operational resource theory (ORT) measure is a nonclassicality measure for bosonic states, notable for its resource-theoretic properties and connection to metrology. However, it can be difficult to evaluate, being linked to an optimization problem for mixed states. Here, we present the first ORT measure calculations for mixed states with photon number coherence. We give exact formulas governing the ORT measure of a broad class of rank-two mixed states, and numerical solutions for some higher-rank states. We also compare the nonclassicality of these states to their metrological power, thus showing in what regimes the metrological power manages to saturate the ORT bound. Throughout, we consider the role of coherence. In particular, we show that nonclassicality and metrological power never increase under bosonic dephasing, but may plateau in a manner similar to entanglement sudden death. Nevertheless, lowering photon number coherence more freely can sometimes yield more nonclassical and metrologically useful states.