论文标题
量子概率的代数来源
Quantum Probability's Algebraic Origin
论文作者
论文摘要
Max Born的统计解释使概率在量子理论中起着重要作用。在这里，我们表明这些量子概率和经典概率具有截然不同的起源。尽管后者始终是由假定的概率度量引起的，但第一个包括具有纯代数来源的过渡概率。此外，此处介绍的过渡概率的一般定义不仅包括纯状态或波浪函数之间众所周知的量子机械过渡概率，而且还包括物理上有意义且可以实验可证实的新型新病例。 与0和1不同的过渡概率以与海森伯格和其他人的不确定性关系相似的方式表现出典型的量子不确定性，此外，以与Bell-Kochen-Specker定理相同的方式排除了确定性状态。但是，此处定义的过渡概率超出了此之外：它表明希尔伯特空间量子逻辑的代数结构决定了某些概率的确切值，并且为这些量子概率提供了意外的访问，而这些量子概率不依赖于状态或波动函数。
Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the latter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the general definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further physically meaningful and experimentally verifiable novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg's and others' uncertainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.
