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arXiv · 1001.2029

Hedged maximum likelihood estimation

Robin Blume-Kohout
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Abstract

This paper proposes and analyzes a new method for quantum state estimation, called hedged maximum likelihood (HMLE). HMLE is a quantum version of Lidstone's Law, also known as the "add beta" rule. A straightforward modification of maximum likelihood estimation (MLE), it can be used as a plugin replacement for MLE. The HMLE estimate is a strictly positive density matrix, slightly less likely than the ML estimate, but with much better behavior for predictive tasks. Single-qubit numerics indicate that HMLE beats MLE, according to several metrics, for nearly all "true" states. For nearly-pure states, MLE does slightly better, but neither method is optimal.

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Robin Blume-Kohout. 2010-01-12. Hedged maximum likelihood estimation. https://doi.org/10.1103/physrevlett.105.200504

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