2013/07/31 by Marcin Jarzyna, Konrad Banaszek, Rafał Demkowicz-Dobrzański +1 · 7 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Coherent states #Dephasing #Fock space #Hilbert space #Limit (mathematics) #Mathematical analysis #Mathematics #Optical Network Technologies #Orbital Angular Momentum in Optics #Photon #Physics #Quantum #Quantum Information and Cryptography #Quantum mechanics #Statistical physics #quant-ph
paper · pdf · doi:10.1088/1751-8113/47/27/275302
published in Journal of Physics A Mathematical and Theoretical 47(27), 275302 (Institute of Physics) · 20 pages, final version
openalex publication_date 2014/06/18 · arxiv created 2014/06/26 · arxiv updated 2014/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyse the ultimate quantum limit on the accessible information for an optical communication scheme when time bins carry coherent light pulses prepared in one of several orthogonal modes and the phase undergoes diffusion after each channel use. This scheme, an example of a quantum memory channel, can be viewed as noisy pulse position modulation (PPM) keying with phase fluctuations occurring between consecutive PPM symbols. We derive a general expression for the output states in the Fock basis and implement a numerical procedure to calculate the Holevo quantity. Using asymptotic properties of Toeplitz matrices, we also present an analytic expression for the Holevo quantity valid for very weak signals and sufficiently strong dephasing when the dominant contribution comes from the single-photon sector in the Hilbert space of signal states. Based on numerical results we conjecture an inequality for contributions to the Holevo quantity from multiphoton sectors which implies that in the asymptotic limit of weak signals, for arbitrarily small dephasing the accessible information scales linearly with the average number of photons contained in the pulse. Such behaviour presents a qualitative departure from the fully coherent case.