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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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Power spectrum of the circular unitary ensemble
Roman Riser, Eugene Kanzieper
- Year
- 2022
- Journal
- arXiv preprint
- DOI
- arXiv:2209.04723
- arXiv
- 2209.04723
We study the power spectrum of eigen-angles of random matrices drawn from the circular unitary ensemble ${\rm CUE}(N)$ and show that it can be evaluated in terms of either a Fredholm determinant, or a Toeplitz determinant, or a sixth Painlevé function. In the limit of infinite-dimensional matrices, $N\rightarrow\infty$, we derive a ${\it\, concise\,}$ parameter-free formula for the power spectrum which involves a fifth Painlevé transcendent and interpret it in terms of the ${\rm Sine}_2$ determinantal random point field. Further, we discuss a universality of the predicted power spectrum law and tabulate it (follow http://eugenekanzieper.faculty.hit.ac.il/data.html) for easy use by random-matrix-theory and quantum chaos practitioners.
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