元胞自动机的量子化
Quantization of Cellular Automata
摘要：
以一个元胞自动机为例，将每个构形看作某个向量空间中的一个基向量，并将全局演化函数线性化。如果幸运的话，这个结果在物理上是有意义的，作为一个有效的量子进化;但是它作为一个量子元胞自动机有意义吗？这是本文所要解决的主要问题.在任何具有离散时间和空间的模型中，要成为一个元胞自动机，需要两个条件：不变性和局部性。我们证明了这种定域性条件在量子情形下是如此严格，以至于每一个以此方式构造的量子元胞自动机- i。例如，通过经典的线性化-必须是可逆的。我们还讨论了一些微妙的非局部性的程度，可以遇到在一维的情况下，我们表明，即使当量化的版本是非本地的，仍然，在某些条件下，我们可能无法使用这种非局部性transmit信息非本地。
英文摘要：
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.
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