关于 Nice Error Bases 的单项性
On the Monomiality of Nice Error Bases
AI总结：
本文否定了每个 nice error basis 是否等价于 shift-and-multiply 基的猜想，但证明总能找到其相当稀疏的表示。
摘要：
酉错误基将 Pauli 矩阵推广到更高维系统。已知酉错误基有两种基本构造：Knill 的代数构造（产生 nice error bases）和 Werner 的组合构造（产生 shift-and-multiply 基）。Schlingemann 和 Werner 提出的一个开放问题将这两种构造联系起来，询问每个 nice error basis 是否等价于 shift-and-multiply 基。我们解决了这个问题并表明答案是否定的。然而，我们也表明，总是可以找到 nice error basis 的一个相当稀疏的表示。
英文摘要：
Unitary error bases generalize the Pauli matrices to higher dimensional systems. Two basic constructions of unitary error bases are known: An algebraic construction by Knill, which yields nice error bases, and a combinatorial construction by Werner, which yields shift-and-multiply bases. An open problem posed by Schlingemann and Werner (see http://www.imaph.tu-bs.de/qi/problems/6.html) relates these two constructions and asks whether each nice error basis is equivalent to a shift-and-multiply basis. We solve this problem and show that the answer is negative. However, we also show that it is always possible to find a fairly sparse representation of a nice error basis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
