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Optimal, reliable estimation of quantum states

Blume-Kohout, Robin (2010) Optimal, reliable estimation of quantum states. New Journal of Physics, 12 (4). Art. No.043034. ISSN 1367-2630.

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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 under certain circumstances it is provably 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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Additional Information:© 2010 IOP Publishing Ltd. Received 7 December 2009. Published 20 April 2010. This paper is the result of more than two years of thinking about state estimation. Much of that thinking has been done out loud, and the author is exceptionally grateful to his conversational partners, in particular, Stephen Bartlett, Carlton Caves, Hartmut Häffner, Patrick Hayden, Richard Gill, Daniel James, Dominik Janzing, Jan Korsbakken, Karan Malhotra, Serge Massar, Colin McCormick, John Preskill, Andrew Silberfarb, Rob Spekkens and Steven Van Enk.
Subject Keywords:Computational physics. Quantum information and quantum mechanics
Issue or Number:4
Classification Code:PACS: 03.67.Lx; 03.65.Yz; 03.65.Wj ; 02.70.Rr; 02.50.-r
Record Number:CaltechAUTHORS:20100518-141828966
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Official Citation:1. Optimal, reliable estimation of quantum states Robin Blume-Kohout 2010 New J. Phys. 12 043034
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18345
Deposited By: Ruth Sustaita
Deposited On:24 Jun 2010 20:55
Last Modified:03 Oct 2019 01:41

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