Robust error bars for quantum tomography

Abstract

In quantum tomography, a quantum state or process is estimated from the results of measurements on many identically prepared systems. Tomography can never identify the state or process exactly. Any point estimate is necessarily "wrong" -- at best, it will be close to the true state. Making rigorous, reliable statements about the system requires region estimates. In this article, I present a procedure for assigning likelihood ratio (LR) confidence regions, an elegant and powerful generalization of error bars. In particular, LR regions are almost optimally powerful -- i.e., they are as small as possible.