Statistical inference with quantum measurements - methodologies for nitrogen vacancy centers in diamond
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2017-11-27 |
| Journal | New Journal of Physics |
| Authors | Ian Hincks, Christopher Granade, David G Cory |
| Citations | 17 |
Abstract
Section titled āAbstractāThe analysis of photon count data from the standard nitrogen vacancy (NV)\nmeasurement process is treated as a statistical inference problem. This has\napplications toward gaining better and more rigorous error bars for tasks such\nas parameter estimation (eg. magnetometry), tomography, and randomized\nbenchmarking. We start by providing a summary of the standard phenomenological\nmodel of the NV optical process in terms of Lindblad jump operators. This model\nis used to derive random variables describing emitted photons during\nmeasurement, to which finite visibility, dark counts, and imperfect state\npreparation are added. NV spin-state measurement is then stated as an abstract\nstatistical inference problem consisting of an underlying biased coin\nobstructed by three Poisson rates. Relevant frequentist and Bayesian estimators\nare provided, discussed, and quantitatively compared. We show numerically that\nthe risk of the maximum likelihood estimator is well approximated by the\nCramer-Rao bound, for which we provide a simple formula. Of the estimators, we\nin particular promote the Bayes estimator, owing to its slightly better risk\nperformance, and straight-forward error propagation into more complex\nexperiments. This is illustrated on experimental data, where Quantum\nHamiltonian Learning is performed and cross-validated in a fully Bayesian\nsetting, and compared to a more traditional weighted least squares fit.\n