On the absence of homogeneous scalar unitary cellular automata
Quantum Physics
2009-10-30 v2 comp-gas
High Energy Physics - Theory
Cellular Automata and Lattice Gases
Abstract
Failure to find homogeneous scalar unitary cellular automata (CA) in one dimension led to consideration of only ``approximately unitary'' CA---which motivated our recent proof of a No-go Lemma in one dimension. In this note we extend the one dimensional result to prove the absence of nontrivial homogeneous scalar unitary CA on Euclidean lattices in any dimension.
Cite
@article{arxiv.quant-ph/9604011,
title = {On the absence of homogeneous scalar unitary cellular automata},
author = {David A. Meyer},
journal= {arXiv preprint arXiv:quant-ph/9604011},
year = {2009}
}
Comments
7 pages, plain TeX, 3 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages); minor changes (including title wording) in response to referee suggestions, also updated references; to appear in Phys. Lett. A