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

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