Operator Spaces, Linear Logic and the Heisenberg-Schrödinger Duality of Quantum Theory
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915279366258688 |
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| author | Lindenhovius, Bert Zamdzhiev, Vladimir |
| author_facet | Lindenhovius, Bert Zamdzhiev, Vladimir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operator Spaces, Linear Logic and the Heisenberg-Schrödinger Duality of Quantum Theory Lindenhovius, Bert Zamdzhiev, Vladimir Logic in Computer Science Quantum Physics 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. |
| title | Operator Spaces, Linear Logic and the Heisenberg-Schrödinger Duality of Quantum Theory |
| topic | Logic in Computer Science Quantum Physics |
| url | https://arxiv.org/abs/2505.06069 |