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

• URL: http://arxiv.org/abs/2511.22992v1
• Date: Fri, 28 Nov 2025 08:52:51 GMT
• Title: No-go theorem for norm-based quantumness-certification with linear functionals
• Authors: Soumyakanti Bose, Yong-Siah Teo, Hyukjoon Kwon, Hyunseok Jeong,
• Abstract summary: We develop a general convex resource-theoretic framework to quantify optical quantumness directly from the norms of linear functionals of quantum states.<n>We establish a no-go theorem demonstrating that no universal measure of quantumness can exist in the absence of optimization.
• Score: 2.8815599572682906
• License: http://creativecommons.org/licenses/by/4.0/
• 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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