Quantum capacity of bosonic dephasing channel

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.

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• Capacities of the covariant Pauli channel
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• The noisy Werner-Holevo channel and its properties
• Energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel
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• Classical capacity of quantum non-Gaussian attenuator and amplifier channels