Optimal Discrimination of Gaussian States by Gaussian Measurements

• URL: http://arxiv.org/abs/2603.12182v1
• Date: Thu, 12 Mar 2026 17:12:33 GMT
• Title: Optimal Discrimination of Gaussian States by Gaussian Measurements
• Abstract summary: We derive a condition that completely determines whether or not there exists an optimal Gaussian measurement achieving the max-relative entropy.<n>When the condition is not met, there is a strict gap between the distinguishability achievable by Gaussian measurements and the unconstrained max-relative entropy.
• Score: 9.157994196176551
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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