Local Hidden-Variable Models Clause Samples

Local Hidden-Variable Models. ‌ Since we are discussing intrinsic non-locality, we could like to show that tripartite intrinsic non- locality and quantum tripartite intrinsic non-locality vanish for tripartite correlations that admit a local hidden-variable model. A tripatite correlation admits a local hidden-variable model if it is of the following form: Σ p(a, b, c|x, y, z) = pΛ(λ)p(a|x, λ)p(b|y, λ)p(c|z, λ), (147) where λ is a local hidden variable. It is known that if a distribution admits such a model, then the model can be reformulated so that all the factor distributions p(a x, λ), p(b y, λ), and p(c z, λ) are deterministic with probabilities equal to either zero or one. In this case, using the classical information λ and the input settings of x, y, and z, an eavesdropper can deduce the outcomes a, b, and c with certainty. Hence, for tripartite intrinsic non-locality and quantum tripartite intrinsic non-locality should vanish for local tripartite correlations.
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