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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A hyper-decoherence map is constructed that produces standard quantum theory from quantum boxes theory, evading the Lee-Selby no-go theorem via relaxations on past signalling and purification uniqueness.
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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.
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Decoherence to quantum theory from a causally-indefinite post-quantum theory
A hyper-decoherence map is constructed that produces standard quantum theory from quantum boxes theory, evading the Lee-Selby no-go theorem via relaxations on past signalling and purification uniqueness.