利用二次高斯和和图态构造任意维的等纠缠基
Construction of Equientangled Bases in Arbitrary Dimensions via Quadratic Gauss Sums and Graph States
摘要：
最近[Karimipour和Memarzadeh，Phys.Rev.A73，012329（2006）]研究了在二分空间中找到一族标准正交基的问题，每个基的维数为$D$，具有以下性质：（i）当某些参数$t$变化时，该族连续地在乘积基和最大纠缠基之间插值，以及（ii）对于固定的$t$，所有的基态都具有相同的纠缠量。作者推导出一个必要条件，并提供了明确的解决方案，但$D \leq 5$的存在性的解决方案，为任意尺寸仍然是一个开放的问题。我们证明，这样的家庭存在于任意尺寸提供两个简单的解决方案，一个采用二次高斯和其他使用图形状态的属性。后者可以推广到具有两个以上的多体等纠缠基。
英文摘要：
Recently [Karimipour and Memarzadeh, Phys. Rev. A 73, 012329 (2006)] studied the problem of finding a family of orthonormal bases in a bipartite space each of dimension $D$ with the following properties: (i) The family continuously interpolates between the product basis and the maximally entangled basis as some parameter $t$ is varied, and (ii) for a fixed $t$, all basis states have the same amount of entanglement. The authors derived a necessary condition and provided explicit solutions for $D \leq 5$ but the existence of a solution for arbitrary dimensions remained an open problem. We prove that such families exist in arbitrary dimensions by providing two simple solutions, one employing the properties of quadratic Gauss sums and the other using graph states. The latter can be generalized to multipartite equientangled bases with more than two parties.
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