On the absence of homogeneous scalar unitary cellular automata
arXiv:quant-ph/9604011 · doi:10.1016/S0375-9601(96)00745-1
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.
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
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