Alternate Forms of the T-Matrix in Quantum State Tomography

TL;DR

This paper introduces three new valid alternative forms of the T-matrix for quantum state tomography, improving the robustness and consistency of the maximum likelihood estimation process for single and multi-qubit states.

Contribution

It derives and analyzes three novel T-matrix forms for quantum state tomography, extending their application from single to multiqubit systems.

Findings

Three new T-matrix forms for single-qubit tomography

Enhanced robustness of MLE fitting process

Generalization to multiqubit state tomography

Abstract

In this paper, we focus on alternate forms of the T-matrix used in the Maximum Likelihood Estimate (MLE) procedure for fitting the experimental data collected in quantum state tomography experiments. In particular, we analyze the single quantum state tomography case, deriving in the process three new valid alternate forms for achieving optimality. These alternative forms then serve as a consistency check, thus enhancing the robustness of the MLE fitting process. One form, in particular, serves as a useful compliment to the standard form normally employed. We subsequently provide a generalization of these forms to the case of multiqubit state tomography.