Degradability of Fermionic Gaussian Channels

TL;DR

This paper characterizes the degradability of fermionic Gaussian channels, revealing that only attenuation or amplitude-damping channels are degradable, which simplifies understanding their quantum capacity.

Contribution

It provides a complete characterization of degradable fermionic Gaussian channels, including a standard form and the identification of only specific channels as degradable.

Findings

Degradable fermionic Gaussian channels are limited to attenuation and amplitude-damping types.

A simple standard form for fermionic Gaussian channels is derived.

The quantum capacity of these channels can be straightforwardly computed.

Abstract

We study the degradability of fermionic Gaussian channels. Fermionic quantum channels are a central building block of quantum information processing with fermions, and the family of Gaussian channels, in particular, is relevant in the emerging field of electron quantum optics and its applications for quantum information. Degradable channels are of particular interest since they have a simple formula that characterizes their quantum capacity. We derive a simple standard form for fermionic Gaussian channels. This allows us to fully characterize all degradable $n$-mode fermionic Gaussian channels. In particular, we show that the only degradable such channels correspond to the attenuation or amplitude-damping channel for qubits.