Introduces essential unitarity as the unique structure-compatible generalization of unitarity to higher-order quantum interfaces in a categorical framework, with all quantum core morphisms satisfying it.
Higher-order causal theories are models of BV-logic
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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.
Defines polyslot pslot[C] and srep[C] constructions on symmetric monoidal categories that reconstruct unitary supermaps and forbid time-loops in composition, with equivalence shown on path-contraction groupoids.
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Essential Unitarity for Higher-Order Quantum Computation
Introduces essential unitarity as the unique structure-compatible generalization of unitarity to higher-order quantum interfaces in a categorical framework, with all quantum core morphisms satisfying it.
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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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Polycategorical Constructions for Unitary Supermaps of Arbitrary Dimension
Defines polyslot pslot[C] and srep[C] constructions on symmetric monoidal categories that reconstruct unitary supermaps and forbid time-loops in composition, with equivalence shown on path-contraction groupoids.