IQI Weekly Seminar

Abstract: Tomographic characterization of large-scale quantum systems -- e.g. N qubits -- is hard. It demands resources (number of measurements, offline data processing time, etc.) that grow
exponentially with the number of qubits. These costs can be reduced by developing reduced models with fewer parameters, but now we need methods to select the best model from various
candidates. This is called statistical model selection, and many standard methods require the models to satisfy a property called local asymptotic normality (LAN). Unfortunately, LAN doesn't
hold for models with boundaries, and quantum tomographic models have boundaries. I'll show how to patch this problem for state tomography by defining a generalization of LAN, metricprojected
LAN (MP-LAN), that explicitly accounts for state space boundaries, and allows us to derive a replacement for the classical Wilks Theorem that predicts the behavior of likelihood
ratios. Conveniently, this derivation also yields an expression for the expected mean-squared error of the maximum likelihood estimate, which can be interpreted as the "statistical
dimension" of the local state space. This interpretation may be useful in devising new quantum compressed sensing protocols based on random measurements.