Quantum capacity of bosonic dephasing channel

TL;DR

This paper investigates the quantum capacity of a non-Gaussian bosonic dephasing channel, deriving a single-letter formula, analyzing the effects of input energy, and characterizing the optimal input states.

Contribution

It provides the first single-letter formula for the quantum capacity of the bosonic dephasing channel and analyzes capacity saturation and decay behaviors.

Findings

Capacity saturates to a finite value with increasing input energy.

Optimal input states are Fock-diagonal with a discrete Gaussian-like distribution.

Quantum capacity decays exponentially at high dephasing rates.

Abstract

We study the quantum capacity of continuous variable dephasing channel, which is a notable example of non-Gaussian quantum channel. We prove that a single letter formula applies. We then consider input energy restriction and show that by increasing it, the capacity saturates to a finite value. The optimal input state is found to be diagonal in the Fock basis and with a distribution that is a discrete version of a Gaussian. Relations between its mean/variance and dephasing rate/input energy are put forward. We also show that quantum capacity decays exponentially for large values of dephasing rates.