Reliable Maximum Likelihood Reconstruction for Quantum Tomography
ABSTRACT :
Quantum tomography is a crucial primitive underlying a multitude of quantum information processing tasks. A reliable estimation strategy requires not only an accurate guess that makes best use of available measurement data, but also a statement about how certain we are of our guess. To this end, I will first present a superfast algorithm to accurately reconstruct the popular maximum-likelihood estimator (MLE) [1]. Then, I will discuss how to put practically meaningful error bars on the MLE [2]. If one is interested only in certain properties of the quantum state, it is important to estimate those quantities directly from the data, rather than first estimating the state; I will briefly explain how to go about this in a reliable manner [3].