一句话：证明算子空间范畴可建模直觉主义与经典线性逻辑，并使其对偶与量子理论的海森堡-薛定谔对偶相容。
本文研究量子理论中的对偶结构与线性逻辑语义之间的联系。作者以算子空间及完全收缩映射构成的范畴 OS 为语义基础，证明该范畴是局部可数可表现的，并构成 Lafont 意义下的直觉主义线性逻辑模型。在此基础上，他们构造了一个基于 OS 的经典线性逻辑模型，其线性逻辑对偶与量子理论的 Heisenberg-Schrödinger 对偶相容。该框架还能统一描述纯态与混合态量子信息、二者的交互，以及量子 switch 等高阶量子映射。
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.
DOI 原文 ·
@inproceedings{paperbot8646,
title = {Operator Spaces, Linear Logic and the Heisenberg-Schrödinger Duality of Quantum Theory},
author = {Bert Lindenhovius and Vladimir Zamdzhiev},
booktitle = {LICS},
year = {2025},
doi = {10.1109/lics65433.2025.00071}
}