一种新的用正交列阵构造纠缠态的方法

A new method for constructing entangled states via orthogonal arrays

对于一个N粒子多体纯态,如果它的所有k粒子约化态是最大混合的,则称为k级均匀态.最近Goyeneche和Zyczkowski提出了一个通过正交列阵构造k级均匀态的方法.本文将提出一种用正交列阵构造量子态的新方法,即增加相位参数的方法.采用同一正交列阵,由我们的新方法所构造的量子态,对于四粒子量子态,发现该量子态不仅是1级均匀态,而且为最大纠缠态;对于五粒子量子态,发现可以使原来的1级均匀态变为2级均匀态.特别地,对于四粒子量子态,用新方法可以构造出许多新形式的最大纠缠态.

A pure quantum state of N subsystems with d levels each is called k-multipartite maximally entangled state, which we call a k-uniform state, if all its reductions to k qubits are maximally mixed. Recently, Goyeneche and Zyczkowski proposed a method of constructing k-uniform states via orthogonal arrays, by which, we will also propose a new method to construct quantum states with orthogonal arrays in this paper, which is the method of increasing phase parameters. We can find the quantum states constructed via our new method by using the same orthogonal array, for four-qubit quantum states, not only are they 1-uniform states, also may become maximally entangled states; for five-qubit quantum states, we find that it can make the original 1-uniform states into 2-uniform states. In particular, for four-qubit quantum states, we can construct a series of new forms of maximally entangled states via our new method.