Quantification of Nonclassicality

TL;DR

This paper introduces an operational and axiomatic framework to quantify single-mode nonclassicality, revealing that certain states can exhibit perfect quantumness under specific measurements, aligning with quantum principles.

Contribution

It presents a novel operational measure of nonclassicality based on measurement negativity and explores its consistency with quantum axioms.

Findings

Moderately squeezed states can show perfect nonclassicality with proper measurements

The proposed measure aligns with the algebraic structure of quantum states

Operational and axiomatic approaches are consistent with quantum principles

Abstract

To quantify single mode nonclassicality, we start from an operational approach. A positive semi-definite observable is introduced to describe a measurement setup. The quantification is based on the negativity of the normally ordered version of this observable. Perfect operational quantumness corresponds to the quantum-noise-free measurement of the chosen observable. Surprisingly, even moderately squeezed states may exhibit perfect quantumness for a properly designed measurement. The quantification is also considered from an axiomatic viewpoint, based on the algebraic structure of the quantum states and the quantum superposition principle. Basic conclusions from both approaches are consistent with this fundamental principle of the quantum world.