Hedged Maximum Likelihood Quantum State Estimation

Robin Blume-Kohout
Phys. Rev. Lett. 105, 200504 – Published 10 November 2010

Abstract

This Letter 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 β” rule. A straightforward modification of maximum likelihood estimation (MLE), it can be used as a plug-in 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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  • Received 17 February 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.200504

© 2010 The American Physical Society

Authors & Affiliations

Robin Blume-Kohout*

  • Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada

  • *robin@blumekohout.com

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Vol. 105, Iss. 20 — 12 November 2010

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