Preliminary investigation of a new state estimation technique using device-independent maximum likelihood estimation

TL;DR

This paper explores a novel quantum state estimation method inspired by device-independent protocols, embedding measurement operators in a Bell scenario and applying a regularized maximum likelihood approach, with preliminary results showing comparable performance to standard methods.

Contribution

Introduces a device-independent maximum likelihood estimation technique for quantum state tomography, integrating Bell scenario frameworks into the estimation process.

Findings

No significant difference observed in reconstructed states using the new method

Method provides an alternative regularization approach for quantum state estimation

Preliminary results suggest potential for further refinement and application

Abstract

In quantum state tomography, the estimated frequencies do not correspond directly to a physical quantum state, due to statistical fluctuations. Thus, one resorts to point estimators that return the state that matches observations the best, and a variety of estimators have been proposed -- linear inversion, least squares, maximum likelihood (ML) -- each making different trade-offs. In this short note, we investigate an alternative approach inspired by device-independent quantum information protocols. We embed a tomographic complete set of measurement operators within the framework of a Bell scenario, and first regularize the estimated frequencies using a device-independent maximum likelihood algorithm. We then run the standard maximum likelihood algorithm to estimate the underlying quantum state. In this preliminary investigation, we do not observe significant differences in the reconstructed state when using the new algorithm.