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arXiv 0908.3408quant-ph
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局域决定论中的纠缠量子态

Entangled quantum states in a local deterministic theory

Gerard 't Hooft

摘要:

研究了元胞自动机中常见的一类模型,发现量子算符可以用来描述它们的长距离行为。这些算符跨越了希尔伯特空间,似乎把这样的模型变成了真正的量子场论,遵守了量子算符的通常定域性条件。纠缠态可以像量子理论那样精确地构造出来。这就提出了一个问题,即这种模型是否允许贝尔不等式被违反。作为一个定域的、确定性的理论,人们会争辩说这是不可能的,但是由于在大的距离尺度上,这个模型似乎与真实的量子场论没有什么不同,所以有理由怀疑为什么它不允许纠缠态。标准的论点有关贝尔的不平等重新审查在这个光。

英文摘要:

Investigating a class of models that is familiar in studies of cellular automata, we find that quantum operators can be employed to describe their long distance behavior. These operators span a Hilbert space that appears to turn such a model into a genuine quantum field theory, obeying the usual conditions of locality in terms of its quantum commutators. Entangled states can be constructed exactly as in quantum theories. This raises the question whether such models allow Bell's inequalities to be violated. Being a local, deterministic theory, one would argue that this is impossible, but since at large distance scales the model does not seem to differ from real quantum field theories, there is reason to wonder why it should not allow entangled states. The standard arguments concerning Bell's inequalities are re-examined in this light.

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