Operational resource theory of continuous-variable nonclassicality

TL;DR

This paper introduces an operational framework to quantify and analyze nonclassicality in continuous-variable quantum states, establishing fundamental constraints and hierarchies for resource manipulation.

Contribution

It develops new measures of nonclassicality based on quantum fluctuations and Fisher information, and derives constraints on nonclassicality concentration in multi-mode states.

Findings

Established no-go results for squeezing concentration.

Defined a hierarchy of nonclassicality for Gaussian states.

Provided fundamental limits on nonclassical resource manipulation.

Abstract

Genuinely quantum states of a harmonic oscillator may be distinguished from their classical counterparts by the Glauber-Sudarshan P-representation -- a state lacking a positive P-function is said to be nonclassical. In this paper, we propose a general operational framework for studying nonclassicality as a resource in networks of passive linear elements and measurements with feed-forward. Within this setting, we define new measures of nonclassicality based on the quantum fluctuations of quadratures, as well as the quantum Fisher information of quadrature displacements. These lead to fundamental constraints on the manipulation of nonclassicality, especially its concentration into subsystems, that apply to generic multi-mode non-Gaussian states. Special cases of our framework include no-go results in the concentration of squeezing and a complete hierarchy of nonclassicality for single mode Gaussian states.