English

On the Cayley digraphs that are patterns of unitary matrices

Combinatorics 2007-05-23 v1 Quantum Physics

Abstract

A digraph D is the pattern of a matrix M when D has an arc ij if and only if the ij-th entry of M is nonzero. Study the relationship between unitary matrices and their patterns is motivated by works in quantum chaology and quantum computation. In this note, we prove that if a Cayley digraph is a line digraph then it is the pattern of a unitary matrix. We prove that for any finite group with two generators there exists a set of generators such that the Cayley digraph with respect to such a set is a line digraph and hence the pattern of a unitary matrix.

Keywords

Cite

@article{arxiv.math/0207079,
  title  = {On the Cayley digraphs that are patterns of unitary matrices},
  author = {Simone Severini},
  journal= {arXiv preprint arXiv:math/0207079},
  year   = {2007}
}
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