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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 choices in estimating quantum states [@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 [@catonibook], we derive rates of convergence for the posterior mean. The numerical performance of these estimators are tested on simulated and real datasets.'
author:
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    The Tien Mai [^1] & Pierre Alquier\
    [CREST, ENSAE, Université Paris Saclay]{}\
    [3 av. Pierre Larousse, 92245 Malakoff CEDEX, France]{}
title: 'Pseudo-Bayesian Quantum Tomography with Rank-adaptation'
---

Introduction
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Playing a vital role in quantum information processing, as well as being fundamental for characterizing quantum objects, quantum state tomography focuses on 