标题： 通过酉误差基的量子隐形传态探索 显示英文标题

标题： Exploring quantum teleportation through unitary error bases

摘要： 酉误差基在量子信息和量子计算中有许多应用，并与量子隐形传态、密集编码和量子纠错密切相关。 Werner 的组合构造从一组哈达玛矩阵和一个拉丁方中构建一个酉误差基。 在本论文中，我给出了拉丁方的新范畴公理化方法，并利用此方法给出 Werner 构造的完全图形化表述和正确性证明。 范畴方法清楚地表明，一些拉丁方公理对于构造的进行是不必要的，我提出了一种推广的构造方案，有可能创建新的酉误差基类别。 显示英文摘要

摘要： Unitary error bases have a great number of applications across quantum information and quantum computation, and are fundamentally linked to quantum teleportation, dense coding and quantum error correction. Werner's combinatorial construction builds a unitary error basis from a family of Hadamard matrices and a Latin square. In this dissertation, I give a new categorical axiomatisation of Latin squares, and use this to give a fully graphical presentation and proof of the correctness of Werner's construction. The categorical approach makes clear that some of the Latin square axioms are unnecessary for the construction to go through, and I propose a generalised construction scheme with the potential to create new classes of unitary error bases.