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Universal bound on the cardinality of local hidden variables in networks
(pp0910-0926)
Denis Rosset, Nicolas Gisin, and Elie Wolfe
doi:
https://doi.org/10.26421/QIC18.11-12-2
Abstracts:
We present an algebraic description of the sets of local
correlations in arbitrary networks, when the parties have finite inputs
and outputs. We consider networks generalizing the usual Bell scenarios
by the presence of multiple uncorrelated sources. We prove a finite
upper bound on the cardinality of the value sets of the local hidden
variables. Consequently, we find that the sets of local correlations are
connected, closed and semialgebraic,
and bounded by tight polynomial Bell-like inequalities.
Key words:
Nonlocality,
Quantum Networks, Causal Structures |