Optimal Discrimination of Mixed Symmetric Multi-mode Coherent States
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909350351601664 |
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| author | Petrongonas, Ioannis Andersson, Erika |
| author_facet | Petrongonas, Ioannis Andersson, Erika |
| contents | We find the optimal measurement for distinguishing between symmetric multi-mode phase-randomized coherent states. A motivation for this is that phase-randomized coherent states can be used for quantum communication, including quantum cryptography. The so-called square-root measurement is optimal for pure symmetric states, but is not always optimal for mixed symmetric states. When phase-randomizing a multi-mode coherent state, the state becomes a mixture of pure multi-mode states with different total photon numbers. We find that the optimal measurement for distinguishing between any set of phase-randomised coherent states can be realised by first counting the total number of photons, and then distinguishing between the resulting pure states in the corresponding photon-number subspace. If the multi-mode coherent states we started from are symmetric, then the optimal measurement in each subspace is a square-root measurement. The overall optimal measurement in the cases we consider is also a square-root measurement. In some cases, we are able to present a simple linear optical circuit that realizes the overall optimal measurement. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_11632 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Discrimination of Mixed Symmetric Multi-mode Coherent States Petrongonas, Ioannis Andersson, Erika Quantum Physics We find the optimal measurement for distinguishing between symmetric multi-mode phase-randomized coherent states. A motivation for this is that phase-randomized coherent states can be used for quantum communication, including quantum cryptography. The so-called square-root measurement is optimal for pure symmetric states, but is not always optimal for mixed symmetric states. When phase-randomizing a multi-mode coherent state, the state becomes a mixture of pure multi-mode states with different total photon numbers. We find that the optimal measurement for distinguishing between any set of phase-randomised coherent states can be realised by first counting the total number of photons, and then distinguishing between the resulting pure states in the corresponding photon-number subspace. If the multi-mode coherent states we started from are symmetric, then the optimal measurement in each subspace is a square-root measurement. The overall optimal measurement in the cases we consider is also a square-root measurement. In some cases, we are able to present a simple linear optical circuit that realizes the overall optimal measurement. |
| title | Optimal Discrimination of Mixed Symmetric Multi-mode Coherent States |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.11632 |