title: Hedged maximum likelihood quantum state estimation.
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.
authors.affiliation: Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada. robin@blumekohout.com
authors.forename: Robin
authors.initials: R
authors.lastname: Blume-Kohout