2025/05/09 by Bert Lindenhovius, Lindenhovius, Bert, Vladimir Zamdzhiev +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Logic in Computer Science (cs.LO) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2505.06069
openalex publication_date 2025/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the category OS of operator spaces, with complete contractions as morphisms, is locally countably presentable and a model of Intuitionistic Linear Logic in the sense of Lafont. We then describe a model of Classical Linear Logic, based on OS, whose duality is compatible with the Heisenberg-Schrödinger duality of quantum theory. We also show that OS provides a good setting for studying pure state and mixed state quantum information, the interaction between the two, and even higher-order quantum maps such as the quantum switch.