Quantization of cellular automata

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Quantization of cellular automata
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 result could actually make sense physically, as a valid quantum evolution; but does it make sense as a quantum cellular automaton? That is the main question we address in this paper. In every model with discrete time and space, two things are required in order to qualify as a cellular automaton: invariance by translation and locality. We prove that this locality condition is so restrictive in the quantum 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 one-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 transmit information nonlocally.
Pablo Arrighi, Vincent Nesme
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2008
Where JAC
Authors Pablo Arrighi, Vincent Nesme
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