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A Profunctorial Semantics for Quantum Supermaps

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arxiv 2402.02997 v2 pith:TWOAUVSM submitted 2024-02-05 quant-ph cs.LOmath.CT

A Profunctorial Semantics for Quantum Supermaps

classification quant-ph cs.LOmath.CT
keywords supermapsblack-boxquantumcausalconcreteconnectivesfactorisationlogical
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We identify morphisms of strong profunctors as a categorification of quantum supermaps. These black-box generalisations of diagrams-with-holes are hence placed within the broader field of profunctor optics, as morphisms in the category of copresheaves on concrete networks. This enables the first construction of abstract logical connectives such as tensor products and negations for supermaps in a totally theory-independent setting. These logical connectives are found to be all that is needed to abstractly model the key structural features of the quantum theory of supermaps: black-box indefinite causal order, black-box definite causal order, and the factorisation of definitely causally ordered supermaps into concrete circuit diagrams. We demonstrate that at the heart of these factorisation theorems lies the Yoneda lemma and the notion of representability.

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  1. Causality in Pure Quantum Computation with Quantum Control

    cs.PL 2026-07 conditional novelty 7.0

    A typed lambda calculus based on intuitionistic BV logic blocks higher-order quantum-control programs that violate causality, and its categorical model excludes the OCB process.