Monday, July 29, 2013

1307.6871 (Marcin Jarzyna et al.)

Dephasing in coherent communication with weak signal states    [PDF]

Marcin Jarzyna, Konrad Banaszek, Rafal Demkowicz-Dobrzanski
We analyze the ultimate quantum limit on the classical capacity of an optical communication scheme when consecutive time bins carry coherent light pulses prepared in one of orthogonal modes and the relative phase between bins undergoes diffusion. 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 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 limit of low average photon number the channel capacity for arbitrarily weak dephasing scales linearly with the average number of photons contained in the pulse. Such behaviour presents a qualitative departure from the fully coherent scheme.
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