Qubit quantum channels: A characteristic function approach

TL;DR

This paper introduces a characteristic function approach to characterize qubit quantum channels, drawing parallels with Bosonic channels and defining Gaussian channels for qubits.

Contribution

It develops a novel characteristic function framework for qubit channels and introduces Gaussian channels with properties similar to Bosonic systems.

Findings

Defined qubit characteristic functions using Grassmann variables

Introduced and characterized Gaussian qubit channels

Established similarities between qubit and Bosonic Gaussian channels

Abstract

A characterization of qubit quantum channels is introduced. In analogy to what happens in the context of Bosonic channels we exploit the possibility of representing the states of the system in terms of characteristic function. The latter are functions of non-commuting variables (Grassmann variables) and are defined in terms of generalized displacement operators. In this context we introduce the set of Gaussian channels and show that they share similar properties with the corresponding Bosonic counterpart.