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arXiv:2511.22992

No-go theorem for norm-based quantumness-certification with linear functionals

Soumyakanti Bose, Yong-Siah Teo, Hyukjoon Kwon, Hyunseok Jeong

quant-phSubmitted Nov 28, 2025• Announced Dec 1, 2025• 0 citations
v1 · Nov 28, 2025v2 · Sep 29, 2026
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Abstract

Despite several approaches proposed to operationally characterize quantum states of light-those that cannot be sampled with a positive distribution over classical states-most existing formulations suffer from limited practicality or rely on convex optimization procedures that are computationally demanding. In this work, we develop a general convex resource-theoretic framework to quantify optical quantumness directly from the norms of linear functionals of quantum states, thereby avoiding any optimization. We further establish a no-go theorem demonstrating that no universal measure of quantumness can exist in the absence of optimization. Finally, we substantiate our theoretical result through explicit examples involving both Gaussian and non-Gaussian states.

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

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The general problem of performance advantage obtainable by the use of nonclassical transmitted states over classical ones is considered. Attention is focused on the situation where system loss is significant and additive Gaussian noise may be present at the receiver. Under the assumption that the total received state is classical, rigorous output density operator representations and their trace distance bounds are developed for classical and nonclassical transmitted states. For applications with high loss in all modes, a practical no-go theorem is enunciated that rules out the possibility of significant advantage of nonclassical over classical states. The recent work on quantum illumination is discussed as an example of our no-go approach.
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