Information criteria for efficient quantum state estimation

TL;DR

This paper introduces an approach for efficient quantum state estimation using information criteria, particularly the Akaike Information Criterion, to verify models with a small number of parameters, demonstrated on noisy Dicke states.

Contribution

It extends quantum state tomography by applying information criteria to validate flexible models with few parameters, enhancing efficiency and applicability.

Findings

The method effectively verifies quantum state models using AIC.

Simulations on noisy Dicke states demonstrate the approach's practicality.

The approach offers a statistically rigorous way to select models in quantum tomography.

Abstract

Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively introducing certain simplifying assumptions on the form of the quantum state, and subsequently using the data to rigorously verify these assumptions. The simplifying assumptions considered so far were (i) the state can be well approximated to be of low rank, or (ii) the state can be well approximated as a matrix product state. We add one more method in that same spirit: we allow in principle any model for the state, using any (small) number of parameters (which can, e.g., be chosen to have a clear physical meaning), and the data are used to verify the model. The proof that this method is valid cannot be as strict as in above-mentioned cases, but is based on well-established statistical methods that go under the name of "information criteria." We exploit here, in particular, the Akaike Information Criterion (AIC). We illustrate the method by simulating experiments on (noisy) Dicke states.