Optimal, reliable estimation of quantum states

Details Optimal, reliable estimation of quantum states Optimal, reliable estimation of quantum states

2006-11-07

arxiv.org/abs/quant-ph/0611080v1

New J. Phys. 12, 043034 (2010)

Physics

Quantum Physics

RevTeX; 14 pages, 2 embedded figures. Comments enthusiastically welcomed!

Scientific paper

10.1088/1367-2630/12/4/043034

Accurately inferring the state of a quantum device from the results of measurements is a crucial task in building quantum information processing hardware. The predominant state estimation procedure, maximum likelihood estimation (MLE), generally reports an estimate with zero eigenvalues. These cannot be justified. Furthermore, the MLE estimate is incompatible with error bars, so conclusions drawn from it are suspect. I propose an alternative procedure, Bayesian mean estimation (BME). BME never yields zero eigenvalues, its eigenvalues provide a bound on their own uncertainties, and it is the most accurate procedure possible. I show how to implement BME numerically, and how to obtain natural error bars that are compatible with the estimate. Finally, I briefly discuss the differences between Bayesian and frequentist estimation techniques.

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