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A joint probability distribution is local whenever it can be written as P (ab | xy) = ? d λ ω (λ) P (a | x, λ) P (b | y, λ), where the classical variable λ is distributed according to the probability distribution ω (λ). This definition easily generalizes to an arbitrary number of parties. Those probability distributions which do not admit this decomposition are said to be nonlocal.
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Actually, our proof also applies for slightly more general protocols in which the local measurements among parties belonging to the same block in the bipartition can be correlated using classical communication. It also applies for situations where parties A1 and Am are projected into any fully nonlocal state (pL=0).
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Actually, our proof also applies for slightly more general protocols in which the local measurements among parties belonging to the same block in the bipartition can be correlated using classical communication. It also applies for situations where parties A 1 and A m are projected into any fully nonlocal state (p L = 0).
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If PNSA,B(a?b?|x?,y?)=0, the nonlocal distribution is not well defined, but the induced state ψ2a?b? is local and our proof still holds.
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If P NS A, B (a? b? | x?, y?) = 0, the nonlocal distribution is not well defined, but the induced state ψ 2 a? b? is local and our proof still holds.
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