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.
A complete logic for causal consistency
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Higher order quantum map types are identified with Boolean type functions, with comb types corresponding to chain posets, and type functions decomposed via max/min of basic chains corresponding to affine mixtures and intersections.
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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.
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On the structure of higher order quantum maps
Higher order quantum map types are identified with Boolean type functions, with comb types corresponding to chain posets, and type functions decomposed via max/min of basic chains corresponding to affine mixtures and intersections.