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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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Entanglement of Free-Fermion Systems, Signal Processing and Algebraic Combinatorics

  • 会议论文

  • 发表日期：

    2025年

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

摘要

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.