2024/10/15 by Ioannis Petrongonas, Petrongonas, Ioannis, Erika Andersson +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #FOS: Physical sciences #Laser-Matter Interactions and Applications #Quantum Physics (quant-ph) #Spectroscopy Techniques in Biomedical and Chemical Research #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2410.11632
openalex publication_date 2024/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.