Dephasing in coherent communication with weak signal states

TL;DR

This paper investigates the quantum limits of information transfer in optical communication with weak signals under phase diffusion, deriving analytical and numerical results that reveal a linear scaling of accessible information with photon number in certain regimes.

Contribution

It provides a new analytical expression for the Holevo quantity in phase-diffused coherent states and conjectures a fundamental inequality affecting information scaling.

Findings

Accessible information scales linearly with photon number at weak signals and small dephasing.

Derived an analytical formula for the Holevo quantity under phase diffusion.

Numerical results support the conjecture about multiphoton sector contributions.

Abstract

We analyze 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.