Quantum state tomography: Mean squared error matters, bias does not

Understand

Because of the constraint that the estimators be bona fide physical states, any quantum state tomography scheme - including the widely used maximum likelihood estimation - yields estimators that may have a bias, although they are consistent estimators.

• Schwemmer et al.
• (arXiv:1310.8465 [quant-ph]) illustrate this by observing a systematic underestimation of the fidelity and an overestimation of entanglement in estimators obtained from simulated data.
• Further, these authors argue that the simple method of linear inversion overcomes this (perceived) problem of bias, and there is the suggestion to abandon time-tested estimation procedures in favor of linear inversion.