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Why Quantum Measurements Yield Single Values
Foundations of Physics ( IF 1.5 ) Pub Date : 2021-02-23 , DOI: 10.1007/s10701-021-00440-1
H. S. Perlman

It is shown that the Born Rule probabilities, i.e. the squares of the moduli of the coefficients in a pure state superposition, refer to mutually exclusive events consequent on measurement. It is also shown that the eigenstates in a pure state superposition are not mutually exclusive events. If the Born Rule is to be retained as the fundamental interpretative postulate of quantum mechanics then it follows, firstly, that the probabilities necessarily refer not to the eigenstates but to the eigenvalues to which the eigenstates belong and, secondly, that the eigenvalues are necessarily mutually exclusive events. This means that to ask why a measurement of an observable on a system in a pure state superposition of eigenstates yields a single state rather than all the states in the superposition is to ill-pose the quantum measurement problem. The events the Born Rule probabilities properly refer to are not states but values. And it also means that the correctly-posed measurement problem, why does a measurement of an observable in a pure state superposition of the eigenstates of the observable yield a single eigenvalue rather than all the eigenvalues implicit in the superposition, admits of the answer: the values, being mutually exclusive events, constitute a statistical mixture of values, and as such, a measurement will yield just one of them.



中文翻译:

为何量子测量产生单一值

结果表明,伯恩法则概率,即在纯态叠加中的系数模的平方,指的是测量结果所导致的互斥事件。还表明,纯态叠加的本征态不是相互排斥的事件。如果要保留伯恩定律作为量子力学的基本解释性假设,那么它首先是,概率不一定是指本征态,而是指本征态所属的本征值;其次,本征值必然是相互的独家活动。这意味着要问为什么在本征态的纯态叠加中对系统上的可观测值的测量会产生单个状态,而不是叠加中的所有状态,这是对量子测量问题的不适。出生规则概率正确引用的事件不是状态而是值。这也意味着正确摆放的测量问题,为什么在可观察的本征态的纯态叠加中对可观察的观测进行测量会产生单个特征值,而不是叠加中隐含的所有本征值?答案是:值是互斥的事件,构成了值的统计混合,因此,度量将仅产生其中之一。

更新日期:2021-02-24
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