A new approach to characterize qubit channels

TL;DR

This paper introduces a novel method for analyzing qubit channels using characteristic functions and Grassmann variables, establishing a parallel with continuous-variable systems and defining qubit Gaussian channels.

Contribution

It presents a new framework for representing qubit channels with characteristic functions, enabling the definition and analysis of qubit Gaussian channels.

Findings

Qubit channels can be represented using characteristic functions with Grassmann variables.

Qubit Gaussian channels share properties with continuous-variable Gaussian channels.

Several examples of qubit channels are analyzed using this new approach.

Abstract

We analyze qubit channels by exploiting the possibility of representing two-level quantum systems in terms of characteristic functions. To do so, we use functions of non-commuting variables (Grassmann variables), defined in terms of generalized displacement operators, following an approach which resemble the one adopted for continuous-variable (Bosonic) systems. It allows us to introduce the notion of qubit Gaussian channels and to show that they share similar properties with the corresponding continuous-variable counterpart. Some examples of qubit channels are investigated using this approach.