论文标题
在多拷贝场景中量子状态的真实多部分纠缠
Genuine multipartite entanglement of quantum states in the multiple-copy scenario
论文作者
论文摘要
真正的多部分纠缠（GME）被认为是一种强大的纠缠形式，因为它与那些不可分配的状态相对应，即\ \ \ \ \ \ \ \跨各方不同两分的部分可分开状态的混合物。在这项工作中，我们在多拷贝制度中研究了这种现象，其中可以产生和控制给定状态的许多完美副本。在这种情况下，上面的定义会导致细微的复杂性，因为可以进行gme-activativations，即\ \ \ \ \ \ \ \ biseparable状态的几个副本可以显示GME。我们表明，一组GME-活化状态可以容纳一个简单的表征：当且仅当双方两者中它不能部分分离时，状态是GME激活的。这导致了第二个问题，即在需要观察GME激活的副本数量中是否存在一般上限，我们以负面的方式回答。特别是，通过提供明确的构造，我们证明，对于任何数量的各方和任何数字$ k \ in \ mathbb {n} $中的任何数字$ k \ in \ mathbb {n} $都存在固定的固定多部分（即\ $ k $）的多部分状态（即\ $ k $），从而使$ k $ cop of biseparable均可保持。
Genuine multipartite entanglement (GME) is considered a powerful form of entanglement since it corresponds to those states that are not biseparable, i.e.\ a mixture of partially separable states across different bipartitions of the parties. In this work we study this phenomenon in the multiple-copy regime, where many perfect copies of a given state can be produced and controlled. In this scenario the above definition leads to subtle intricacies as biseparable states can be GME-activatable, i.e.\ several copies of a biseparable state can display GME. We show that the set of GME-activatable states admits a simple characterization: a state is GME-activatable if and only if it is not partially separable across one bipartition of the parties. This leads to the second question of whether there is a general upper bound in the number of copies that needs to be considered in order to observe the activation of GME, which we answer in the negative. In particular, by providing an explicit construction, we prove that for any number of parties and any number $k\in\mathbb{N}$ there exist GME-activatable multipartite states of fixed (i.e.\ independent of $k$) local dimensions such that $k$ copies of them remain biseparable.
