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Person# Chun Lam Chan

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Jean François Emmanuel Barbier, Chun Lam Chan, Nicolas Macris

Recently, a new adaptive path interpolation method has been developed as a simple and versatile scheme to calculate exactly the asymptotic mutual information of Bayesian inference problems defined on dense factor graphs. These include random linear and generalized estimation, sparse superposition codes, and low-rank matrix / tensor estimation. For all these systems, the adaptive interpolation method directly proves that the replica-symmetric prediction is exact, in a simple and unified manner. When the underlying factor graph of the inference problem is sparse the replica prediction is considerably more complicated, and rigorous results are often lacking or obtained by rather complicated methods. In this work we show how to extend the adaptive path interpolation method to sparse systems. We concentrate on a censored block model, where hidden variables are measured through a binary erasure channel, for which we fully prove the replica prediction.

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In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies th

Bayesian inference (ˈbeɪziən or ˈbeɪʒən ) is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes avail

Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deductio

Samuel Bosch, Chun Lam Chan, Su Yeon Chang, Marc-André Dupertuis, Frédéric Gessler, Nicolas Macris, Nicolas Schwaller

We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell diagonal states is generated, and several characteristic indicators, namely entanglement of formation and concurrence, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work, we also find a remarkable general inequality between “quantum discord” and “asymmetric relative entropy of discord”: the former never exceeds the latter. We also prove that for all BDS the two coincide.

2021Jean François Emmanuel Barbier, Chun Lam Chan, Nicolas Macris

We consider mean field ferromagnetic spin models on dilute random graphs and prove that, with suitable one-body infinitesimal perturbations added to the Hamiltonian, the multi-overlaps concentrate for all temperatures, both with respect to the thermal Gibbs average and the quenched randomness. Results of this nature have been known only for the lowest order overlaps, at high temperature or on the Nishimori line. Here we treat all multi-overlaps by a non-trivial application of Griffiths-Kelly-Sherman correlation inequalities. Our results apply in particular to the pure and mixedp-spin ferromagnets on random dilute Erdoes-Renyi hypergraphs. On physical grounds one expects that multi-overlap concentration is an important ingredient for the validity of the cavity (or replica-symmetric) formula for the pressure of mean field models. However rigorously establishing this formula for thep-spin ferromagnet on a random dilute hypergraph remains an open problem.