arXiv 2203.093572022-03-27quant-ph

Kochen和Specker关于函数关系的观点与崩溃假设相冲突

Kochen and Specker's view on functional relations conflicts with the collapse postulate

Alisson Tezzin

备注：: 16 pages

摘要：

Kochen-Specker定理的一个关键组成部分是所谓的函数合成原理，它断言隐藏状态必须以与它们之间的所有函数关系一致的方式将值赋予可观测值。这个原理的动机是假设，像经典力学中的可观测量的函数一样，量子理论中的可观测量A的函数$g(A)$只是从$A$导出的逻辑上可能的可观测量，并且测量$g(A)$包括测量$A$和通过$g$后处理结果值。在本文中，我们表明，在适当的条件下，这个合理的假设是在冲突的崩溃公设。然后，我们讨论了可能的解决方案，这一冲突，我们认为，最合理的和不那么激进的一个包括在适应崩溃假设考虑到测量的背景。这种对上下文的依赖性的产生，与为什么柯亨-斯派克定理排除了非上下文隐变量模型的原因完全相同，即可观测量A通常可以写成非对易可观测量$B,C$的函数$A=g(B)=h(C)$。

英文摘要：

A key ingredient of the Kochen-Specker theorem is the so-called functional composition principle, which asserts that hidden states must ascribe values to observables in a way that is consistent with all functional relations between them. This principle is motivated by the assumption that, like functions of observables in classical mechanics, a function $g(A)$ of an observable A in quantum theory is simply a logically possible observable derived from $A$, and that measuring $g(A)$ consists in measuring $A$ and post-processing the resulting value via $g$. In this paper we show that, under suitable conditions, this reasonable assumption is in conflict with the collapse postulate. We then discuss possible solutions to this conflict, and we argue that the most justifiable and less radical one consists in adapting the collapse postulate by taking measurement contexts into account. This dependence on contexts arises for precisely the same reason why noncontextual hidden-variable models are ruled out by the Kochen-Specker theorem, namely that an observable A can typically be written as a function $A=g(B)=h(C)$ of noncommuting observables $B,C$.

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