Tomographic portrait of quantum channels

TL;DR

This paper explores quantum channels within the quantum tomography framework, deriving kernels for qubit and bosonic systems, and reveals that Gaussian quantum channels correspond to non-Gaussian classical channels.

Contribution

It introduces a tomography-based formulation of quantum channels and characterizes their classical stochastic map counterparts for specific quantum systems.

Findings

Derived kernels for qubit and bosonic quantum channels

Single mode Gaussian quantum channels map to non-Gaussian classical channels

Provides a framework linking quantum channels to classical stochastic maps

Abstract

We formulate the notion of quantum channels in the framework of quantum tomography and address there the issue of whether such maps can be regarded as classical stochastic maps. In particular kernels of maps acting on probability representation of quantum states are derived for qubit and bosonic systems. In the latter case it results that a single mode Gaussian quantum channel corresponds to non-Gaussian classical channels.