Accuracy of quantum-state estimation utilizing Akaike’s information criterion

Abstract

We report our theoretical and experimental investigations into errors in quantum-state estimation, putting a special emphasis on their asymptotic behavior. Tomographic measurements and maximum likelihood estimation are used for estimating several kinds of identically prepared quantum states (biphoton polarization states) produced via spontaneous parametric down-conversion. Excess errors in the estimation procedures are eliminated by introducing an estimation strategy utilizing Akaike's information criterion. We make a quantitative comparison between the errors of the experimentally estimated states and their asymptotic lower bounds, which are derived from the Cram\'er-Rao inequality. Our results reveal the influence of entanglement on the errors in the estimation. An alternative measurement strategy employing inseparable measurements is also discussed, and its performance is numerically explored.