Calibrated hypergraphs and multi-qudit states are shown to form graded Ω monads, providing a categorical foundation for a broad generalization of hypergraph states.
Bell Inequalities for Graph States
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abstract
We investigate the non-local properties of graph states. To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, for each graph state there is an inequality maximally violated only by that state. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positivity of the partial transpose or the geometric measure of entanglement.
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Calibrated hypergraph states: I calibrated hypergraph and multi qudit state monads
Calibrated hypergraphs and multi-qudit states are shown to form graded Ω monads, providing a categorical foundation for a broad generalization of hypergraph states.