For Bell scenarios where N-1 parties have two binary measurements, all quantum correlations can be realized with local dimensions 2 for those parties and 2^(N-1) for the last, up to a Carathéodory factor.
Upper bounds on violation of Bell-type inequalities by a multipartite quantum state
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We present the new exact upper bounds on the maximal Bell violation for the generalized N-qubit GHZ state, the N-qudit GHZ state and, in general, for an arbitrary N-partite quantum state, possibly infinite-dimensional. Our results indicate that, for an N-partite quantum state of any Hilbert space dimension, violation of any Bell-type inequality (either on correlation functions or on joint probabilities) with S settings and any number of outcomes at each site cannot exceed (2S-1)^{N-1}.
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Upper Bounding Hilbert Space Dimensions which can Realize all the Quantum Correlations
For Bell scenarios where N-1 parties have two binary measurements, all quantum correlations can be realized with local dimensions 2 for those parties and 2^(N-1) for the last, up to a Carathéodory factor.