title: Minimax Quantum Tomography: Estimators and Relative Entropy Bounds.
abstract: A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O(1/sqrt[N])-in contrast to that of classical probability estimation, which is O(1/N)-where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. This makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states.
authors.affiliation: Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA.|Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia.
authors.forename: Christopher
authors.initials: C
authors.lastname: Ferrie
authors.affiliation: Center for Computing Research (Sandia National Laboratories), Albuquerque, New Mexico 87185, USA.
authors.forename: Robin
authors.initials: R
authors.lastname: Blume-Kohout