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arXiv 1012.2122quant-ph
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宏观实在论隐含着测量的语境性

Measurement contextuality is implied by macroscopic realism

Zeqian Chen, Alberto Montina

摘要:

量子力学的本体论理论提供了一个现实的描述,通过定义良好的量调节测量结果的单一系统。为了完整,它们还应该满足宏观实在论的最低条件。在结果决定论的假设下,当Hilbert空间维数大于2时,它们都被证明是投射测度的上下文。近年来,一个广义的非语境性概念被引入,也适用于结果不确定性和非尖锐测量的情况。指出Beltrametti-Bugajski模型是测量非语境非决定论的一个例子。在这里,我们提供了一个简单的证明,这个模型是唯一一个具有这样的功能,投影测量和希尔伯特空间维数大于2。作为一个推论,冯诺依曼测量的非情境性意味着非锐化测量的非情境性。通过指出Beltrametti-Bugajski模型不满足宏观实在论的条件,我们得出结论:在本体论理论框架下解决测量问题的唯一途径是放松广义意义上的非语境性假设。

英文摘要:

Ontological theories of quantum mechanics provide a realistic description of single systems by means of well-defined quantities conditioning the measurement outcomes. In order to be complete, they should also fulfil the minimal condition of macroscopic realism. Under the assumption of outcome determinism and for Hilbert space dimension greater than two, they were all proved to be contextual for projective measurements. In the recent years a generalized concept of non-contextuality was introduced that applies also to the case of outcome indeterminism and unsharp measurements. It was pointed out that the Beltrametti-Bugajski model is an example of measurement non-contextual indeterminist theory. Here we provide a simple proof that this model is the only one with such a feature for projective measurements and Hilbert space dimension greater than two. As a corollary, von Neumann measurement non-contextuality implies non-contextuality for unsharp measurements. By noting that the Beltrametti-Bugajski model does not satisfy the condition of macroscopic realism, we arrive at the conclusion that the only way to solve the measurement problem in the framework of an ontological theory is relaxing the hypothesis of non-contextuality in its generalized sense.

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