Effect algebras, presheaves, non-locality and contextuality
نویسندگان
چکیده
منابع مشابه
Effect Algebras, Presheaves, Non-locality and Contextuality
Non-locality and contextuality are among the most counterintuitive aspects of quantum theory. They are difficult to study using classical logic and probability theory. In this paper we start with an effect algebraic approach to the study of non-locality and contextuality. We will see how different slices over the category of set valued functors on the natural numbers induce different settings i...
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We discuss quantum non-locality and contextuality using the notion of transition sets [1, 2]. This approach provides a way to obtain a direct logical contradiction with locality/non-contextuality in the EPRB gedanken experiment as well as a clear graphical illustration of what violations of Bell inequalities quantify. In particular, we show graphically how these violations are related to measur...
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In a previous paper with Adam Brandenburger, we used sheaf theory to analyze the structure of non-locality and contextuality. Moreover, on the basis of this formulation, we showed that the phenomena of non-locality and contextuality can be characterized precisely in terms of obstructions to the existence of global sections. Our aim in the present work is to build on these results, and to use th...
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Locality and non-contextuality are intuitively appealing features of classical physics, which are contradicted by quantum mechanics. The goal of the classic no-go theorems by Bell, Kochen-Specker, et al. is to show that non-locality and contextuality are necessary features of any theory whose predictions agree with those of quantum mechanics. We use the mathematics of sheaf theory to analyze th...
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A number of landmark results in the foundations of quantum mechanics show that quantum systems exhibit behaviour that defies explanation in classical terms, and that cannot be accounted for in such terms even by postulating “hidden variables” as additional unobserved factors. Much has been written on these matters, but there is surprisingly little unanimity even on basic definitions or the inte...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2018
ISSN: 0890-5401
DOI: 10.1016/j.ic.2018.02.012