We define generalised notions of biunitary elements in planar algebras and show that objects arising in quantum information theory such as Hadamard matrices, quantum latin squares and unitary error bases are all given by biunitary elements in the spin planar algebra. We show that there are natural subfactor planar algebras associated with biunitary elements.

中文翻译：

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平面代数、量子信息论和子因子

我们定义了平面代数中二元元素的广义概念，并表明量子信息理论中出现的对象，如哈达玛矩阵、量子拉丁方和酉误差基，都是由自旋平面代数中的二元元素给出的。我们表明存在与二元元素相关的自然子因子平面代数。