The Born rule as structure of spectral bundles (extended abstract)
The Born rule as structure of spectral bundles (extended abstract)
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DOI：
10.4204/eptcs.95.8
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发表时间：
2012-10
期刊：
影响因子：
--
通讯作者：
B. Fauser;Guillaume Raynaud;S. Vickers
中科院分区：
文献类型：
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作者：
B. Fauser;Guillaume Raynaud;S. Vickers
量子基础的拓扑方法通过谱束以统一的方式描述，其中基础空间是上下文空间，每条光纤都是其光谱。方差的差异是由于束是纤维化或反纤维化造成的。相对于这种结构，有限维设置中玻恩规则的概率预测被描述为一组估值的一部分。该结构在本质上利用了评估区域单子的几何性质。
Topos approaches to quantum foundations are described in a unified way by means of spectral bundles, where the base space is a space of contexts and each fibre is its spectrum. Differences in variance are due to the bundle being a fibration or opfibration. Relative to this structure, the probabilistic predictions of the Born rule in finite dimensional settings are then described as a section of a bundle of valuations. The construction uses in an essential way the geometric nature of the valuation locale monad.