Optimal Discrimination of Gaussian States by Gaussian Measurements
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912963514859520 |
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| author | Turner, Leah Lami, Ludovico Guta, Madalin Adesso, Gerardo |
| author_facet | Turner, Leah Lami, Ludovico Guta, Madalin Adesso, Gerardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12182 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Discrimination of Gaussian States by Gaussian Measurements Turner, Leah Lami, Ludovico Guta, Madalin Adesso, Gerardo Quantum Physics 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. |
| title | Optimal Discrimination of Gaussian States by Gaussian Measurements |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.12182 |