Foundational Structures and Methods for Quantum Informatics

量子力学为信息处理提供了全新的可能性，其中纠缠（在空间分离的粒子之间存在强瞬时关联的可能性，导致高度违反直觉的非局域效应）等现象发挥了核心作用。目前处理这些想法以及量子系统与其经典观察者之间微妙的相互作用和信息流的方法都很繁琐，在这个提议中，在我们以前的工作的基础上，我们的目标是使用在计算机科学中已经证明有用的思想和方法来开发一个优雅的概念方法，既用于量子力学本身的基础，也用于量子信息处理系统的描述，设计和分析。其效果就像是拥有一种高级编程语言-在这种语言中，“计算机”就是物理世界！虽然我们使用的基本数学（范畴论）是相当抽象的，它伴随着一个非常直观的图解形式主义，这是有用的，作为一个实用的工具计算，这种形式主义还导致了与逻辑的迷人和意想不到的联系--我们的图表可以被看作是形式证明的图形表示--和几何概念，如结和辫子。

Quantum Mechanics offers radically new possibilities for information processing, with phenomena such as entanglement --- the possibility of strong instantaneous correlations between spatially separated particles, leading to highly counter-intuitive non-local effects --- playing a central role.Current methods for dealing with these ideas, and with the subtle interplays and information flows between a quantum system and its classical observer, are cumbersome, and somewhat like the early days of programming computers in machine code.In this proposal, building on our previous work, we aim to use ideas and methods which have already proved useful in Computer Science to develop an elegant, conceptual approach, both to the foundations of Quantum Mechanics itself, and to the description, design and analysis of quantum information processing systems. The effect is something like having a high-level programming language --- in which the `computer' is the physical world!While the underlying mathematics we use (category theory) is quite abstract, it is accompanied by a very intuitive diagrammatic formalism, which is useful both as a practical tool for calculations, and for bringing the ideas to life in a very vivid and visual fashion.This formalism also leads to fascinating and unexpected links with logic --- our diagrams can be seen as graphical representations of formal proofs --- and with geometric ideas such as knots and braids.