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Logic and Algebraic Structures in Quantum Computing by Valentina Harizanov, Ali Eskandarian, Jennifer Chubb

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FIBER PRODUCTS OF MEASURES AND QUANTUM FOUNDATIONS

ADAM BRANDENBURGER AND H. JEROME KEISLER

Abstract. With a view to quantum foundations, we define the concepts of an empirical model (a probabilistic model describing measurements and outcomes), a hidden-variable model (an empirical model augmented by unobserved variables), and various properties of hidden-variable models, for the case of infinite measurement spaces and finite outcome spaces. Thus, our framework is general enough to include, for example, quantum experiments that involve spin measurements at arbitrary relative angles. Within this framework, we use the concept of the fiber product of measures to prove general versions of two determinization results about hidden-variable models. ...

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