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arXiv 1005.2242quant-ph
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量子测度与共事件解释

Quantum measures and the coevent interpretation

Stan Gudder

摘要:

本文首先回顾了量子测度和积分理论。给出了量子积分的一种新表示。通过计算一些量子(勒贝格)${}^2$积分来说明这种表示。本文的其余部分只考虑有限空间。讨论了非同态逻辑,研究了共事件的经典定义域。考虑了纯量子测度和共事件,证明了纯量子测度严格包含在以1为上界的量子测度集的极值元中。证明了有限事件空间$\ascript$上的任何量子测度都可以转化为非同态逻辑$\ascript ^*$上的普通测度。这样,$\ascript$上的量子动力学可以用更大空间$\ascript ^*$上的经典动力学来描述。

英文摘要:

This paper first reviews quantum measure and integration theory. A new representation of the quantum integral is presented. This representation is illustrated by computing some quantum (Lebesgue)${}^2$ integrals. The rest of the paper only considers finite spaces. Anhomomorphic logics are discussed and the classical domain of a coevent is studied. Pure quantum measures and coevents are considered and it is shown that pure quantum measures are strictly contained in the extremal elements for the set of quantum measures bounded above by one. Moreover, we prove that any quantum measure on a finite event space $\ascript$ can be transferred to an ordinary measure on an anhomomorphic logic $\ascript ^*$. In this way, the quantum dynamics on $\ascript$ can be described by a classical dynamics on the larger space $\ascript ^*$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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