冯·诺依曼定理的意外重现
Unexpected reemergence of von Neumann theorem
摘要：
这里表明，arXiv：0704.1962的“单一系统量子性的简单测试”（最近的实验实现见arXiv：0804.1646）与冯·诺依曼定理（1932）的讨论具有完全相同的关系，即通过经典概率方案（即隐变量或现实理论）描述量子系统的问题。后一个由Bell（1966）证明，源于一个假设，即对于每个单独的系统，两个非对易观测量之和（也是一个观测量）的隐变量值必须等于两个算子的本征值之和。人们找不到一个物理理由来证明这样一个假设对不可比较的变量成立。从积极的方面来说。该准则可用于拒绝基于随机经典场的模型。然而，作者所使用的例子具有经典的光学实现。
英文摘要：
Is is shown here that the "simple test of quantumness for a single system" of arXiv:0704.1962 (for a recent experimental realization see arXiv:0804.1646) has exactly the same relation to the discussion of to the problem of describing the quantum system via a classical probabilistic scheme (that is in terms of hidden variables, or within a realistic theory) as the von Neumann theorem (1932). The latter one was shown by Bell (1966) to stem from an assumption that the hidden variable values for a sum of two non-commuting observables (which is an observable too) have to be, for each individual system, equal to sums of eigenvalues of the two operators. One cannot find a physical justification for such an assumption to hold for non-commeasurable variables. On the positive side. the criterion may be useful in rejecting models which are based on stochastic classical fields. Nevertheless the example used by the Authors has a classical optical realization.
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