A simple representation of quantum process tomography

TL;DR

This paper introduces a simplified approach to quantum process tomography using the Fano representation, making the process more intuitive and directly related to measurable quantities in quantum systems.

Contribution

It demonstrates that the Fano representation yields a real, minimal-parameter quantum process matrix directly linked to expectation value evolution, simplifying quantum process characterization.

Findings

The Fano representation matrix is real and has a number of elements equal to the free parameters.

The matrix elements are directly related to the evolution of expectation values.

Examples include one- and two-qubit quantum noise channels.

Abstract

We show that the Fano representation leads to a particularly simple and appealing form of the quantum process tomography matrix $\chi_{_F}$, in that the matrix $\chi_{_F}$ is real, the number of matrix elements is exactly equal to the number of free parameters required for the complete characterization of a quantum operation, and these matrix elements are directly related to evolution of the expectation values of the system's polarization measurements. These facts are illustrated in the examples of one- and two-qubit quantum noise channels.