Abstract
In Brandenburger and Keisler ([2012b]) we showed that, provided only that the measurement and outcome spaces in an experimental system are measure-theoretically separable, then there is a canonical hidden-variable space, namely the unit interval equipped with Lebesgue measure. Here, we use this result to establish a general relationship between two kinds of conditions on correlations in quantum systems: Bell locality ([1964]) and λ-independence on the one hand, and no signaling (Ghirardi, Rimini, and Weber ([1980]), Jordan ([1983])) on the other hand.
This chapter was prepared for the symposium in honor of the 60th birthday of Samson Abramsky. Work with Samson Abramsky, Lucy Brandenburger, Andrei Savochkin, and Noson Yanofsky was an important input into the current work. The authors are grateful to two referees and the volume editor for valuable feedback, and to the NYU Stern School of Business for financial support.
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Brandenburger, A., Keisler, H.J. (2013). Use of a Canonical Hidden-Variable Space in Quantum Mechanics. In: Coecke, B., Ong, L., Panangaden, P. (eds) Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Lecture Notes in Computer Science, vol 7860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38164-5_1
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