论文标题
非正交量子状态表示的测量结果之间的非古典关系的表征
Characterization of the non-classical relation between measurement outcomes represented by non-orthogonal quantum states
论文作者
论文摘要
量子力学描述了无法共同执行的测量结果之间看似自相矛盾的关系。在希尔伯特（Hilbert）空间中，这种不兼容的测量结果由非正交状态表示。在本文中，我们调查了非正交量子状态代表的结果之间的关系与不取决于实际测量环境的测量结果的联合分配所暗示的关系有所不同。该分析是基于一个众所周知的场景，在该场景中，关于某些结果的不可能的三个陈述似乎也使特定的第四次结果不可能，但是量子理论允许以非呈现的可能性观察该结果。我们表明，希尔伯特空间形式主义通过定义第四个概率的下限来改变四个测量结果之间的关系，而第四个概率的下限随着前三个结果的总概率下降到零而增加。因此，量子理论使得违反了测量结果之间的非上下文一致性，不仅可能成为可能，而且实际上要求它是希尔伯特空间内部产品的必要结果，这些结果描述了不同测量结果之间的上下文关系。
Quantum mechanics describes seemingly paradoxical relations between the outcomes of measurements that cannot be performed jointly. In Hilbert space, the outcomes of such incompatible measurements are represented by non-orthogonal states. In this paper, we investigate how the relation between outcomes represented by non-orthogonal quantum states differs from the relations suggested by a joint assignment of measurement outcomes that do not depend on the actual measurement context. The analysis is based on a well-known scenario where three statements about the impossibilities of certain outcomes would seem to make a specific fourth outcome impossible as well, yet quantum theory allows the observation of that outcome with a non-vanishing probability. We show that the Hilbert space formalism modifies the relation between the four measurement outcomes by defining a lower bound of the fourth probability that increases as the total probability of the first three outcomes drops to zero. Quantum theory thus makes the violation of non-contextual consistency between the measurement outcomes not only possible, but actually requires it as a necessary consequence of the Hilbert space inner products that describe the contextual relation between the outcomes of different measurements.
