论文标题
纠缠传递性问题
Entanglement transitivity problems
论文作者
论文摘要
科学的目标之一是了解整个部分与其部分之间的关系，这是由证明从其减少状态的知识来证明系统的纠缠的问题所用的。在这里，我们关注一个不同但相关的问题：边际信息的集合可以揭示新的边缘信息吗？我们肯定地回答了这一点，并表明（非）纠缠边缘状态可以表现出（元）纠缠的传递性，即暗示必须纠缠不同的目标边缘。通过证明与某些与某些双Qubit边缘兼容的全局$ n $ qubit状态是独特的，我们证明存在涉及任意大量量子的系统的传递性。我们还完全表征 - 在提供必要的条件和充分条件的意义上 - 当（元）传递性在三方情况下发生时，当给出的两个问题的边缘是Werner状态或各向异性状态时。我们的数值结果表明，在三方场景中，纠缠传递性是从纯状态得出的边缘的一般性。
One of the goals of science is to understand the relation between a whole and its parts, as exemplified by the problem of certifying the entanglement of a system from the knowledge of its reduced states. Here, we focus on a different but related question: can a collection of marginal information reveal new marginal information? We answer this affirmatively and show that (non-) entangled marginal states may exhibit (meta)transitivity of entanglement, i.e., implying that a different target marginal must be entangled. By showing that the global $n$-qubit state compatible with certain two-qubit marginals in a tree form is unique, we prove that transitivity exists for a system involving an arbitrarily large number of qubits. We also completely characterize -- in the sense of providing both the necessary and sufficient conditions -- when (meta)transitivity can occur in a tripartite scenario when the two-qudit marginals given are either the Werner states or the isotropic states. Our numerical results suggest that in the tripartite scenario, entanglement transitivity is generic among the marginals derived from pure states.
