Tensors, !-graphs, and non-commutative quantum structures (extended version)
Logic in Computer Science
2015-03-05 v1 Category Theory
Quantum Physics
Abstract
!-graphs provide a means of reasoning about infinite families of string diagrams and have proven useful in manipulation of (co)algebraic structures like Hopf algebras, Frobenius algebras, and compositions thereof. However, they have previously been limited by an inability to express families of diagrams involving non-commutative structures which play a central role in algebraic quantum information and the theory of quantum groups. In this paper, we fix this shortcoming by offering a new semantics for non-commutative !-graphs using an enriched version of Penrose's abstract tensor notation.
Cite
@article{arxiv.1503.01348,
title = {Tensors, !-graphs, and non-commutative quantum structures (extended version)},
author = {Aleks Kissinger and David Quick},
journal= {arXiv preprint arXiv:1503.01348},
year = {2015}
}
Comments
extended version of arXiv:1412.8552 [cs.LO], adds additional examples and soundness proofs