Optimal, reliable estimation of quantum states
- Creators
- Blume-Kohout, Robin
Abstract
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.
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.Attached Files
Published - BlumeKohout2010p9962New_J_Phys.pdf
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Additional details
- Eprint ID
- 18345
- Resolver ID
- CaltechAUTHORS:20100518-141828966
- Created
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2010-06-24Created from EPrint's datestamp field
- Updated
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2022-07-12Created from EPrint's last_modified field