论文标题
$ K $ - 统一状态和量子信息掩蔽
$k$-Uniform states and quantum information masking
论文作者
论文摘要
如果将所有减少到$ k $ partions的削减最大混合在一起，则具有本地尺寸$ d $的$ n $派对的纯净状态称为$ k $统一状态。根据$ k $均匀状态，正交阵列和线性代码之间的连接，我们为$ k $均匀的状态提供了一般构造。我们表明，当$ d \ geq 4K-2 $（resp。$ d \ geq 2k-1 $）是主要功率时，对于任何$ n \ geq 2k $（$ 2k \ leq n \ leq n \ leq d+1 $），存在$ k $ - 统一状态。特别是，我们几乎每$ n $ qudits都有$ 4,5 $统一的状态。此外，我们将量子信息掩盖的概念概述在由[modi \ emph {et al。} {phys提供的两部分系统中。莱特牧师。 \ textbf {120}，230501（2018）}]至$ k $ - 均匀的量子信息掩盖多部分系统，我们表明$ k $ - 均匀的状态和量子错误纠正型代码可用于$ k $ - 均匀统一的量子量子掩模。
A pure state of $N$ parties with local dimension $d$ is called a $k$-uniform state if all the reductions to $k$ parties are maximally mixed. Based on the connections among $k$-uniform states, orthogonal arrays and linear codes, we give general constructions for $k$-uniform states. We show that when $d\geq 4k-2$ (resp. $d\geq 2k-1$) is a prime power, there exists a $k$-uniform state for any $N\geq 2k$ (resp. $2k\leq N\leq d+1$). Specially, we give the existence of $4,5$-uniform states for almost every $N$-qudits. Further, we generalize the concept of quantum information masking in bipartite systems given by [Modi \emph{et al.} {Phys. Rev. Lett. \textbf{120}, 230501 (2018)}] to $k$-uniform quantum information masking in multipartite systems, and we show that $k$-uniform states and quantum error-correcting codes can be used for $k$-uniform quantum information masking.
