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.

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

arXiv:2511.22992 [quant-ph]

(or arXiv:2511.22992v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2511.22992 Focus to learn more arXiv-issued DOI via DataCite

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