Quantifying nonclassicality of mixed Fock states

TL;DR

This paper introduces a linear programming approach to quantify the nonclassicality of mixed Fock states in bosonic modes, revealing phase distinctions based on populations and enabling analysis of higher-rank states.

Contribution

It presents a novel, efficient method to evaluate nonclassicality of mixed states using resource theory and linear programming, with analytical insights for specific cases.

Findings

Nonclassicality can be characterized by a convex roof measure.

The problem reduces to a linear programming formulation.

Distinct phases depend on the populations of neighboring Fock states.

Abstract

Nonclassical states of bosonic modes are important resources for quantum-enhanced technologies. Yet, quantifying nonclassicality of these states, in particular mixed states, can be a challenge. Here we present results of quantifying the nonclassicality of a bosonic mode in a mixed Fock state via the operational resource theory (ORT) measure [W. Ge, K. Jacobs, S. Asiri, M. Foss-Feig, and M. S. Zubairy, Phys. Rev. Res. 2, 023400 (2020)], which relates nonclassicality to metrological advantage. Generally speaking, evaluating a resource-theoretic measure for mixed states is challenging, since it involves finding a convex roof. However, we show that our problem can be reduced to a linear programming problem. By analyzing the results of numerical optimization, we are able to extract analytical results for the case where three or four neighboring Fock states have nonzero population. Interestingly, we find that such a mode can be in distinct phases, depending on the populations. Lastly, we demonstrate how our method is generalizable to density matrices of higher ranks. Our findings suggest a viable method for evaluating nonclassicality of arbitrary mixed bosonic states and potentially for solving other convex roof optimization problems.