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QI: Fachverband Quanteninformation
QI 24: Verification and Benchmarking of Quantum Systems
QI 24.12: Vortrag
Donnerstag, 21. März 2024, 12:45–13:00, HFT-TA 441
Pathological Behavior of Point Estimators with Minimum Bias (in Quantum Tomography, etc.) — •Yien Liang1,2,3 and Matthias Kleinmann1 — 1Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany — 2Peking University, Beijing 100871, China — 3Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany
Being unbiased can be a desirable property for a statistical point estimator, that is, that the mean estimated value of a parameter coincides with the actual value of the parameter. While this property can be traded for other desiderata, it has been noted that in quantum physics, specifically in quantum state tomography, any estimator that always yields a physical estimate is necessarily biased. This affects the possible meaning of a state estimator, however, only if this effect is sizable enough to warrant a discussion. So far, no quantitative account of this effect was given and it could be possible that the bias of such an estimator is arbitrary small. Here we ask a more general question concerning the quantitative account of the minimum bias in situations where no unbiased estimator is available. For the example of Bernoulli trails with a constrained parameter space, we find that the least biased estimator is unique, but also pathological, in a certain sense.
Keywords: Point Estimator; Statistical Inference; Quantum Tomography