Calibrated hypergraphs and multi-qudit states are shown to form graded Ω monads, providing a categorical foundation for a broad generalization of hypergraph states.
Quantum secret sharing with qudit graph states
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abstract
We present a unified formalism for threshold quantum secret sharing using graph states of systems with prime dimension. We construct protocols for three varieties of secret sharing: with classical and quantum secrets shared between parties over both classical and quantum channels.
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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.