Teleportation, braid group and Temperley-Lieb algebra
Teleportation, braid group and Temperley-Lieb algebra
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DOI：
10.1088/0305-4470/39/37/017
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发表时间：
2006-09
期刊：
影响因子：
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通讯作者：
Yong Zhang
中科院分区：
文献类型：
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作者：
Yong Zhang
我们通过应用辫群和坦珀利-利布代数来探索量子隐形传态现象背后的代数和拓扑结构。我们在传送的标准描述中实现了辫子传送配置、传送交换和虚拟辫子表示。我们设计了涉及最大纠缠态的量子电路的图解规则，并将其应用于隐形传态的三种描述：转移算子、量子测量和特征方程，并进一步提出局域酉变换下的坦珀利-李布代数作为隐形传态的数学结构。我们将我们的图解方法与量子信息流的两种已知方法进行比较：隐形传态拓扑和强紧凑封闭类别，以便将我们的图解规则解释为隐形传态的自然图解语言。
We explore algebraic and topological structures underlying the quantum teleportation phenomena by applying the braid group and Temperley–Lieb algebra. We realize the braid teleportation configuration, teleportation swapping and virtual braid representation in the standard description of the teleportation. We devise diagrammatic rules for quantum circuits involving maximally entangled states and apply them to three sorts of descriptions of the teleportation: the transfer operator, quantum measurements and characteristic equations, and further propose the Temperley–Lieb algebra under local unitary transformations to be a mathematical structure underlying the teleportation. We compare our diagrammatical approach with two known recipes to the quantum information flow: the teleportation topology and strongly compact closed category, in order to explain our diagrammatic rules to be a natural diagrammatic language for the teleportation.