标题： 关于纽结和量子力学的教程 显示英文标题

标题： A Tutorial on Knots and Quantum Mechanics

摘要： 这些笔记回顾了以空间拓扑为基础的量子力学描述，基于拓扑量子场论和路径积分形式主义的公理。 在此描述中，量子态和算符由用于构建量子力学模型的模块的空间拓扑编码，而期望值和概率则由空间、纽结和链环的拓扑不变量给出。 这些笔记重点在于拓扑如何编码量子力学特征的具体方式，或者等价地，这些特征如何通过拓扑进行控制。 讨论了纠缠的拓扑分类以及纠缠熵的性质和基本量子协议。 主要目的是建立一种不太常见的关于量子力学的图示直觉，扩展“量子图示主义”的范式。 显示英文摘要

摘要： These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by the topology of spaces that are used as modules to build the quantum mechanical model, while expectation values and probabilities are given by topological invariants of spaces, knots and links. The notes focus on the specific way the topology encodes quantum mechanical features, or, equivalently, on how these features can be controlled through the topology. A topological classification of entanglement is discussed, as well as properties of entanglement entropy and basic quantum protocols. The primary aim is to build a less conventional diagrammatic intuition about quantum mechanics, expanding the paradigm of ``Quantum Picturalism".