任意维的等纠缠基与二次高斯和
Equientangled Bases in Arbitrary Dimensions and Quadratic Gauss Sums
摘要：
最近[Karimipour and Memarzadeh，PhysRevA 73，012329（2006）]提出了在两个相同系统的二分空间中找到具有以下性质的正交基的连续族的问题：i）在每个基中，所有状态必须相等地纠缠，以及ii）该族连续地内插在乘积基和最大纠缠基之间。作者提供了一个必要条件和简单的例子，相对较小的尺寸，但质疑存在一个普遍的解决方案，为任意尺寸。利用二次高斯和的性质，我们证明了这样一个家庭的基地存在的所有维度，并提供了一个明确的简单的参数化。我们说明我们的解决方案与特定的例子的行为。
英文摘要：
Recently [Karimipour and Memarzadeh, PhysRevA 73, 012329 (2006)] posed the problem of finding a continuous family of orthonormal bases in a bipartite space of two identical systems with the following properties: i) in each basis, all states have to be equally entangled, and ii) the family continuously interpolate between the product basis and the maximally entangled basis. The authors provided a necessary condition and simple examples for relatively small dimensions, but questioned the existence of a general solution for arbitrary dimensions. Employing the properties of quadratic Gauss sums, we prove that such a family of bases exists for all dimensions and provide an explicit simple parametrization. We illustrate the behaviour of our solution with particular examples.
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