Entanglement of free-fermion systems, signal processing and algebraic combinatorics Article Swipe

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Pierre-Antoine Bernard , Nicolas Crampé , Rafael I. Nepomechie , Gilles Parez , Luc Vinet ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2401.07150

This paper offers a review of recent studies on the entanglement of free-fermion systems on graphs that take advantage of methods pertaining to signal processing and algebraic combinatorics. On the one hand, a parallel with time and band limiting problems is used to obtain a tridiagonal matrix commuting with the chopped correlation matrix in bispectral situations and on the other, the irreducible decomposition of the Terwilliger algebra arising in the context of $P$-polynomial association schemes is seen to yield a simplifying framework.

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Context (archaeology) Algebraic number Quantum entanglement Tridiagonal matrix Algebra over a field Matrix (chemical analysis) Decomposition Mathematics Polynomial Computer science Pure mathematics Quantum mechanics Eigenvalues and eigenvectors Physics Geography Composite material Archaeology Quantum Biology Ecology Materials science Mathematical analysis

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2401.07150
PDF: https://arxiv.org/pdf/2401.07150
OA Status: green
Cited By: 4
Related Works: 10
OpenAlex ID: https://openalex.org/W4391011334

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DOI: https://doi.org/10.48550/arxiv.2401.07150

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Title: Entanglement of free-fermion systems, signal processing and algebraic combinatorics

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-01-13

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Authors: Pierre-Antoine Bernard, Nicolas Crampé, Rafael I. Nepomechie, Gilles Parez, Luc Vinet

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Landing page: https://arxiv.org/abs/2401.07150

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Concepts: Context (archaeology), Algebraic number, Quantum entanglement, Tridiagonal matrix, Algebra over a field, Matrix (chemical analysis), Decomposition, Mathematics, Polynomial, Computer science, Pure mathematics, Quantum mechanics, Eigenvalues and eigenvectors, Physics, Geography, Composite material, Archaeology, Quantum, Biology, Ecology, Materials science, Mathematical analysis

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Cited by: 4

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Citations by year (recent): 2025: 2, 2024: 2

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