No-Go Theorem for Norm-Based Nonclassicality Certification with Linear Functionals

Abstract

Despite various approaches to encode nonclassical light, most existing formulations either suffer from limited practicality or rely on optimization procedures that are computationally demanding. Here, we develop a framework for quantifying optical nonclassicality without invoking any optimization, using generic classicalization channels, p-norms and linear functionals generated by displaced rotationally-invariant operators. However, for a subset of such measures, involving s-ordered distributions and a Gaussian classicalization channel, we analytically establish a no-go theorem demonstrating that no such universal measure can exist. We further substantiate our theoretical result through explicit examples involving both Gaussian and non-Gaussian states, followed by a generic criterion for a no-go theorem, whose the existence remains to be established.

arXiv comment11 pages, 2 figures. Any scientific suggestion/comment(s) are welcome