论文标题
绝对最大的纠结状态等效性，并针对36名欧拉官员的问题建设无限量子解决方案
Absolutely maximally entangled state equivalence and the construction of infinite quantum solutions to the problem of 36 officers of Euler
论文作者
论文摘要
通过其纠缠内容对多部分量子状态进行订购和分类仍然是一个空旷的问题。一类高度纠缠的状态，在量子信息协议中有用，绝对最大的纠缠（AME），非常难以比较，因为它们的所有子系统都是最大的随机随机。虽然众所周知，没有四个Qubit的AME状态，但已知许多分析示例和数值生成的集合。但是，我们证明了令人惊讶的结果，确实只有{\ em One} ame状态四个Qutrits，直到局部统一等效性。相反，对于较大的局部维度，AME状态的局部统一类别的数量被证明是无限的。特别感兴趣的是地方维度6的情况下，最近确定确实存在一个四方AME州，为36名官员的经典不可能的Euler问题提供了量子解决方案。基于此，构建了无穷大的量子解决方案，我们证明这些溶液不是等效的。开发的方法可以被有效地概括为任何数量的粒子的多部分状态。
Ordering and classifying multipartite quantum states by their entanglement content remains an open problem. One class of highly entangled states, useful in quantum information protocols, the absolutely maximally entangled (AME) ones, are specially hard to compare as all their subsystems are maximally random. While, it is well-known that there is no AME state of four qubits, many analytical examples and numerically generated ensembles of four qutrit AME states are known. However, we prove the surprising result that there is truly only {\em one} AME state of four qutrits up to local unitary equivalence. In contrast, for larger local dimensions, the number of local unitary classes of AME states is shown to be infinite. Of special interest is the case of local dimension 6 where it was established recently that a four-party AME state does exist, providing a quantum solution to the classically impossible Euler problem of 36 officers. Based on this, an infinity of quantum solutions are constructed and we prove that these are not equivalent. The methods developed can be usefully generalized to multipartite states of any number of particles.
