Operator Spaces, Linear Logic and the Heisenberg-Schrödinger Duality of Quantum Theory

• URL: http://arxiv.org/abs/2505.06069v1
• Date: Fri, 09 May 2025 14:12:00 GMT
• Title: Operator Spaces, Linear Logic and the Heisenberg-Schrödinger Duality of Quantum Theory
• Authors: Bert Lindenhovius, Vladimir Zamdzhiev,
• Abstract summary: We show that the category OS of operator spaces, with complete contractions as morphisms, is locally countably presentable.<n>We then describe a model of Classical Linear Logic, based on OS, whose duality is compatible with the Heisenberg-Schr"odinger duality of quantum theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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-Schr\"odinger 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.

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