Journal
PHYSICAL REVIEW LETTERS
Volume 105, Issue 20, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.105.200504
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Funding
- Government of Canada (through Industry Canada)
- Province of Ontario (through the Ministry of Research Innovation)
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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 beta 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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