Higher-order quantum map types form a distributive lattice of regular subtypes where signalling relations are determined by type function evaluations and structure poset rank parity, with normal forms derived from maximal chains.
Notice that the diagram has two maximal chains, which we will identify by the sequence of their labels as∅ −1−2 and∅ −3−4
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Order structure and signalling in higher order quantum maps
Higher-order quantum map types form a distributive lattice of regular subtypes where signalling relations are determined by type function evaluations and structure poset rank parity, with normal forms derived from maximal chains.