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Paper 1

Quantum d-separation and quantum belief propagation

Robert R. Tucci

Year

2020

Journal

arXiv preprint

DOI

arXiv:2012.09635

arXiv

2012.09635

The goal of this paper is to generalize classical d-separation and classical Belief Propagation (BP) to the quantum realm. Classical d-separation is an essential ingredient of most of Judea Pearl's work. It is crucial to all 3 rungs of what Pearl calls the 3 rungs of Causation. So having a quantum version of d-separation and BP probably implies that most of Pearl's Bayesian networks work, including his theory of causality, can be translated in a straightforward manner to the quantum realm.

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Paper 2

On the absence of bound states for a planar massless Brown-Ravenhall-type operator

M. B. Alves, O. M. Del Cima, D. H. T. Franco

Year

2022

Journal

arXiv preprint

DOI

arXiv:2209.04559

arXiv

2209.04559

We address the question of the existence of bound states for a suitably projected two-dimensional massless Dirac operator in the presence of a Bessel-Macdonald potential (also known as $K_0$-potential potential), raised by De Lima, Del Cima and Miranda, in Eur.Phys.J. B (2020) 93, 187. Based on Relativistic Hardy Inequality, we prove that this operator has no bound states if $γ\leqslant γ_{\rm crit}$ (subcritical region), where $γ$ is a coupling constant.

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