期刊
NEW JOURNAL OF PHYSICS
卷 20, 期 -, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/aa9c9f
关键词
nitrogen vacancy centers; statistical inference; quantum measurements; quantum Hamiltonian learning
资金
- Canada First Research Excellence Fund (CFREF) Canadian Excellence Research Chairs (CERC)
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Canadian Institute for Advanced Research
- Province of Ontario
- Industry Canada
The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (e.g. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of the standard phenomenological model of the NV optical process in terms of Lindblad jump operators. This model is used to derive random variables describing emitted photons during measurement, to which finite visibility, dark counts, and imperfect state preparation are added. NVspin-state measurement is then stated as an abstract statistical inference problem consisting of an underlying biased coin obstructed by three Poisson rates. Relevant frequentist and Bayesian estimators are provided, discussed, and quantitatively compared. We show numerically that the risk of the maximum likelihood estimator is well approximated by the Cramer-Rao bound, for which we provide a simple formula. Of the estimators, we in particular promote the Bayes estimator, owing to its slightly better risk performance, and straightforward error propagation into more complex experiments. This is illustrated on experimental data, where quantum Hamiltonian learning is performed and cross-validated in a fully Bayesian setting, and compared to a more traditional weighted least squares fit.
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