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27 April 2024 |
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Topological Test Spaces | | Alexander Wilce
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28 May 2004 | | Subject: | quant-ph | | Abstract: | A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with incommensurable random quantities. In the case of quantum mechanics, the relevant test space, the set of orthonormal bases of a Hilbert space, carries significant topological structure. This paper inaugurates a general study of topological test spaces. Among other things, we show that any topological test space with a compact space of outcomes is of finite rank. We also generalize results of Meyer and Clifton-Kent by showing that, under very weak assumptions, any second-countable topological test space contains a dense semi-classical test space. | | Source: | arXiv, quant-ph/0405178 | | Services: | Forum | Review | PDF | Favorites | |
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