Bell态的量子代数
Quantum Algebras Associated With Bell States
摘要：
辫子杨-巴克斯特方程的反对称解称为Bell矩阵，它可以从乘积态产生所有的Bell态，因而在量子信息理论中引起人们的兴趣。本文通过Bell矩阵的FRT构造来研究量子代数。在其二维表示的余积的四维表示中，我们发现了包含二维表示的合成级数和直和的代数结构来刻画这个量子代数。我们还利用Bell矩阵的Yang--FRT化构造了量子代数。
英文摘要：
The antisymmetric solution of the braided Yang--Baxter equation called the Bell matrix becomes interesting in quantum information theory because it can generate all Bell states from product states. In this paper, we study the quantum algebra through the FRT construction of the Bell matrix. In its four dimensional representations via the coproduct of its two dimensional representations, we find algebraic structures including a composition series and a direct sum of its two dimensional representations to characterize this quantum algebra. We also present the quantum algebra using the FRT construction of Yang--Baxterization of the Bell matrix.
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