Pseudo-Bayesian Quantum Tomography with Rank-adaptation

The Tien Mai; Pierre Alquier

doi:10.1016/j.jspi.2016.11.003

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arXiv · 1605.05933

Pseudo-Bayesian Quantum Tomography with Rank-adaptation

The Tien Mai·Pierre Alquier

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Abstract

Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the good and reliable choice in estimating quantum states~\cite{blume2010optimal}. Several numerical works showed that Bayesian estimations are comparable to, and even better than other methods in the problem of $1$-qubit state recovery. However, the problem of choosing prior distribution in the general case of $n$ qubits is not straightforward. More importantly, the statistical performance of Bayesian type estimators have not been studied from a theoretical perspective yet. In this paper, we propose a novel prior for quantum states (density matrices), and we define pseudo-Bayesian estimators of the density matrix. Then, using PAC-Bayesian theorems, we derive rates of convergence for the posterior mean. The numerical performance of these estimators are tested on simulated and real datasets.

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The Tien Mai, Pierre Alquier. 2016-05-19. Pseudo-Bayesian Quantum Tomography with Rank-adaptation. https://doi.org/10.1016/j.jspi.2016.11.003

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