SAMOP 2023 – scientific programme
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QI: Fachverband Quanteninformation
QI 6: Poster I (joint session QI/Q)
QI 6.3: Poster
Monday, March 6, 2023, 16:30–19:00, Empore Lichthof
Reducing Bias in Quantum State Tomography — •Yien Liang1,2 and Matthias Kleinmann1 — 1Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany — 2Peking University, Beijing 100871, China
Quantum state tomography aims to estimate the quantum state of a system using quantum measurements. It is well known that such an estimate cannot be perfect, that is, the procedure may yield an operator with negative eigenvalues or the mean reconstructed state deviates from true state. This is the dilemma of having a nonphysical reconstruction or a biased estimator. It also has been shown that any unbiased estimator has to yield rather large negative eigenvalues. We ask the complementary question: What is the minimum bias of an estimator, even if one is willing to accept an increased variance of the estimator? We show that the bias can indeed be improved by orders of magnitude, but at the price of being rather pathological. We furthermore discuss the behavior of estimators with low bias compared to canonical estimators for large sample sizes and many qubits.