2022/04/22 by A. S. Holevo, Holevo, A. S.
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2204.10626
openalex publication_date 2022/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper we give proof that the information-transmission capacity of the approximate position measurement with the oscillator energy constraint, which underlies noisy Gaussian homodyning in quantum optics, is attained on Gaussian encoding. The proof is based on general principles of convex programming. Rather remarkably, for this particular model the method reduces the solution of the optimization problem to a generalization of the celebrated log-Sobolev inequality. We hope that this method should work also for other models lying out of the scope of the "threshold condition" ensuring that the upper bound for the capacity as a difference between the maximum and the minimum output entropies is attainable.