标题： 四量子比特纯码的分类和五量子比特绝对最大纠缠态 显示英文标题

标题： Classification of four-qubit pure codes and five-qubit absolutely maximally entangled states

摘要： 我们证明了每个5量子比特绝对最大纠缠(AME)态通过局部幺正变换等价于唯一((5,2,3))量子纠错码C中的一个点。此外，C中的两个点等价当且仅当它们由作用在C上的阶为24的群相关联。存在一个由3个不变多项式组成的集合，可以区分5量子比特AME态的等价类。 我们还表明每个4量子比特纯码等价于唯一((4,4,2))的一个子空间，并构造了一个无限族3均匀n量子比特态，其中n为偶数$n\geq 6$。 证明大量依赖于Vinberg和经典不变量理论的结果。 显示英文摘要

摘要： We prove that every 5-qubit absolutely maximally entangled (AME) state is equivalent by a local unitary transformation to a point in the unique ((5,2,3)) quantum error correcting code C. Furthermore, two points in C are equivalent if and only if they are related by a group of order 24 acting on C. There exists a set of 3 invariant polynomials that separates equivalence classes of 5-qubit AME states. We also show that every 4-qubit pure code is equivalent to a subspace of the unique ((4,4,2)) and construct an infinite family of 3-uniform n-qubit states for even $n\geq 6$. The proofs rely heavily on results from Vinberg and classical invariant theory.