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An important problem in quantum information theory is to understand whatmakes entangled quantum systems non-local or hard to simulate efficiently. Inthis work we consider situations in which various parties have access to arestricted set of measurements on their particles, and construct entangledquantum states that are essentially classical for those measurements. Inparticular, given any set of local measurements on a large enough Hilbert spacewhose dual strictly contains (i.e. contains an open neighborhood of) a purestate, we use the PEPS formalism and ideas from generalized probabilistictheories to construct pure multiparty entangled states that have (a) localhidden variable models, and (b) can be efficiently simulated classically. Webelieve that the examples we construct cannot be efficiently classicallysimulated using previous techniques. Without the restriction on themeasurements, the states that we construct are non-local, and in someproof-of-principle cases are universal for measurement based quantumcomputation.

Families of pure PEPS with efficiently simulatable local hidden variable models for most measurements