论文标题
Schur-Weyl国家建设的新方法
A new approach to the construction of Schur-Weyl states
论文作者
论文摘要
Schur-Weyl状态属于一个特殊类别的状态，其对称性由两个年轻和Weyl Tableaux描述。在这些状态上跨越希尔伯特空间中物理系统的表示，可以提取隐藏在非本地自由度的量子信息。在量子计算中，尤其是在量子算法结构中，这种属性在广泛的问题中非常有用，因此了解这些状态的确切形式非常重要。此外，它们允许显着减少本本本特征的大小，或者通常会减少任何物理量的表示矩阵，这些矩阵在对称或统一组代数中表示。在这里，我们提出了一种新的Schur-Weyl状态在自旋链系统表示中构建的新方法。我们的方法是基于基本转移运算符，从中可以为U型组构建Clebsch-Gordan系数，然后得出适当的Schur-Weyl状态概率幅度。
The Schur-Weyl states belong to a special class of states with a symmetry described by two Young and Weyl tableaux. Representation of physical systems in Hilbert space spanned on these states enables to extract quantum information hidden in nonlocal degrees of freedom. Such property can be very useful in a broad range of problems in Quantum Computations, especially in quantum algorithms constructions, therefore it is very important to know exact form of these states. Moreover, they allow to reduce significantly the size of eigenproblem, or in general, diminishing the representation matrix of any physical quantities, represented in the symmetric or unitary group algebra. Here we present a new method of Schur-Weyl states construction in a spin chain system representation. Our approach is based on the fundamental shift operators out of which one can build Clebsch-Gordan coefficients for the unitary group U(n) and then derive appropriate Schur-Weyl state probability amplitudes.
