In this talk I will sketch a project which aims at the design of systematic and efficient procedures to infer quantum models from measured data. Progress in experimental control have enabled an increasingly fine tuned probing of the quantum nature of matter, e.g., in superconducting qubits. Such experiments have shown that we not always have a good understanding of how to model the experimentally performed measurements via POVMs. It turns out that the ad hoc postulation of POVMs can lead to inconsistencies. For example, when doing asymptotic state tomography via linear inversion, one sometimes recovers density operators which are significantly not positive semidefinite. Assuming the asymptotic regime, we suggest an alternative procedure where we do not make a priori assumptions on the quantum model, i.e., on the Hilbert space dimension, the prepared states or the measured POVMs. In other words, we simultaneously estimate the dimension of the underlying Hilbert space, the quantum states and the POVMs. We are guided by Occam's razor, i.e., we search for the minimal quantum model consistent with the data.


Talk Number PIRSA:12120042
Collection Quantum Information