Optimal Discrimination of Gaussian States by Gaussian Measurements

Abstract:Are Gaussian measurements enough to distinguish between Gaussian states? Here, we tackle this question by focusing on the max-relative entropy as an operational distinguishability metric. Given two general multimode Gaussian states, we derive a condition, based on their covariance matrices, that completely determines whether or not there exists an optimal Gaussian measurement achieving the max-relative entropy. When the condition is satisfied, we find this optimal measurement explicitly. When the condition is not met, there is a strict gap between the distinguishability achievable by Gaussian measurements and the unconstrained max-relative entropy in which all measurements are allowed. We illustrate our results in the single-mode setting, and show examples of states for which this gap can be made arbitrarily large, revealing novel instances of Gaussian data hiding.

7 pages, 1 figure. v2: operational interpretation added

arXiv:2603.12182 [quant-ph]

(or arXiv:2603.12182v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.12182 Focus to learn more arXiv-issued DOI via DataCite

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