Quantization of Cellular Automata
| dc.creator | Arrighi, Pablo | |
| dc.creator | Nesme, Vincent | |
| dc.date | 2009-03-02 | |
| dc.date.accessioned | 2026-07-07T12:48:08Z | |
| dc.date.available | 2026-07-07T12:48:08Z | |
| dc.description | Take a cellular automaton, consider that each configuration is a basis vector in some vector space, and linearize the global evolution function. If lucky, the r esult could actually make sense physically, as a valid quantum evolution; but do es it make sense as a quantum cellular automaton? That is the main question we a ddress in this paper. In every model with discrete time and space, two things ar e required in order to qualify as a cellular automaton: invariance by translatio n and locality. We prove that this locality condition is so restrictive in the q uantum case that every quantum cellular automaton constructed in this way - i. e., by linearization of a classical one - must be reversible. We also discuss some subtleties about the extent of nonlocality that can be encountered in the o ne-dimensional case; we show that, even when the quantized version is non local, still, under some conditions, we may be unable to use this nonlocality to trans mit information nonlocally. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0903.0258 | |
| dc.identifier | http://arxiv.org/abs/0903.0258 | |
| dc.identifier | proceedings of JAC 2008, pp. 204-215 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221950 | |
| dc.subject | Quantum Physics | |
| dc.title | Quantization of Cellular Automata | |
| dc.type | text |