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Tsirelson’s Problem and Kirchberg’s Conjecture
, 2010
"... This document is an extended abstract of [Fri10b]. See [JNP + 10] for closely related results obtained by different methods. Quantum correlations in composite quantum systems. In the study of quantum entanglement and quantum correlations, one usually assumes that the state space of a composite quant ..."
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This document is an extended abstract of [Fri10b]. See [JNP + 10] for closely related results obtained by different methods. Quantum correlations in composite quantum systems. In the study of quantum entanglement and quantum correlations, one usually assumes that the state space of a composite quantum system is a tensor product HA ⊗ HB, so that the correlations take on the form P (a, b  x, y) = 〈ψ, (A a x ⊗ B b y)ψ〉. (1) with POVM observables Ax a and B y b. However, how is this justified from physical principles? Can we really be sure that this tensor product assumption is appropriate? One possible alternative assumption might be to say that a composite system is defined in terms of a joint Hilbert space H together with, for each site, a set of local observables on H, such that each observable located on the first site commutes with each observable located on the second site; in physical terms, this means that the observables located at different sites are compatible, and can in particular be measured jointly. This is the “commutativity assumption”. In the case of finitedimensional case, this is effectively equivalent to the
Universal and exotic generalizes fixedpoint algebras for weakly proper actions and duality
 arXiv:1304.5697v2, 2013. 52 PAUL BAUM, ERIK GUENTNER, AND RUFUS WILLETT
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ON THE REPRESENTATION OF A DISCRETE GROUP Γ WITH SUBGROUP Γ0 IN THE CALKIN ALGEBRA OF ℓ2(Γ/Γ0)
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