Perturbational approach to the quantum capacity of additive Gaussian quantum channel

TL;DR

This paper demonstrates that for additive Gaussian quantum channels, the thermal noise state maximizes quantum capacity at high energies, with non-Gaussian perturbations providing no advantage in the first order approximation.

Contribution

It proves that thermal states optimize quantum capacity for such channels at high energies, extending the result to non-Gaussian inputs in the first order perturbation framework.

Findings

Thermal noise states achieve maximum one shot capacity at high energies.

Non-Gaussian perturbations do not improve quantum information transmission in the first order.

The result applies to multiple copies of the input state, indicating robustness of thermal states as optimal inputs.

Abstract

For a quantum channel with additive Gaussian quantum noise, at the large input energy side, we prove that the one shot capacity is achieved by the thermal noise state for all Gaussian state inputs, it is also true for non-Gaussian input in the sense of first order perturbation. For a general case of $n$ copies input, we show that up to first order perturbation, any non-Gaussian perturbation to the product thermal state input has a less quantum information transmission rate when the input energy tend to infinitive.