k-uniform quantum states arising from orthogonal arrays
k-uniform quantum states arising from orthogonal arrays
复制标题
由正交阵列产生的 k 均匀量子态
DOI：
10.1103/physreva.99.042332
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发表时间：
2019-04-25
影响因子：
2.9
通讯作者：
Wang, Yan-Ling
中科院分区：
文献类型：
--
作者：
Li, Mao-Sheng;Wang, Yan-Ling
局部维数为d的N个子系统的纯量子态，如果每次约简到k个量子位都是最大混合，则称为k均匀态。基于一种特殊的组合设计，即无冗余正交阵列，我们证明了当N >= 4且d为非2的素数幂时，2-均匀N-量子态的存在性。此外，给定任意阶大于4的Hadamard矩阵，我们演示了如何使用它来构造3-均匀多量子位态。事实上，我们发现除了N = 9的情况外，当N >= 8时，存在一些3均匀的N量子位。这就回答了Goyeneche等人提出的一个问题。[j].农业工程学报，2014,32(1)。此外，从最小支持k-一致状态出发，我们展示了如何生成由k-一致状态组成的正交基。最后，我们从单个k-均匀N-qudit状态导出了一系列(k - 1)-均匀(N - 1)-qudit状态。在多部纠缠态中，k均匀态是很好的候选态。
A pure quantum state of N subsystems with local dimension d is called a k-uniform state if every reduction to k qudits is maximally mixed. Based on a special class of combinatorial design, namely irredundant orthogonal arrays, we show the existence of 2-uniform N-qudit states when N >= 4 and d is a prime power other than 2. In addition, given any Hadamard matrix of order greater than 4, we demonstrate how it can be used to construct 3-uniform multiqubit states. In fact, we find that there exists some 3-uniform N-qubit when N >= 8 except case N = 9. These give an answer to a question posed by Goyeneche et al. [Phys. Rev. A 90, 022316 (2014)]. Furthermore, starting from a minimal support k-uniform state, we show how to generate an orthogonal basis consisting of k-uniform states. At last, we derive a series of (k - 1)-uniform (N - 1)-qudit states from a single k-uniform N-qudit state. The k-uniform states are good candidates among the multipartite entangled states.