Almost all four-particle pure states are determined by their two-body marginals
Almost all four-particle pure states are determined by their two-body marginals
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DOI：
10.1103/physreva.96.010102
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发表时间：
2017-03
影响因子：
2.9
通讯作者：
Nikolai Wyderka;Felix Huber;O. Guhne
中科院分区：
文献类型：
--
作者：
Nikolai Wyderka;Felix Huber;O. Guhne
我们证明了具有相同内维的四个粒子的一般纯态(根据Haar度量绘制的态)在所有其他纯态中由它们的两体边缘唯一地确定。事实上，两体边缘中的三个的某些子集就足以进行表征。我们还讨论了将这一陈述推广到更多粒子的纯态，表明在纯态中，这些几乎总是由它们的三个$(n-2)$体边缘决定的。最后，我们给出了一类特殊的对称纯四粒子态，它们共享相同的两体边缘，因此是未知的。这些是与广义GHz态叠加的四量子比特Dicke态。
We show that generic pure states (states drawn according to the Haar measure) of four particles of equal internal dimension are uniquely determined among all other pure states by their two-body marginals. In fact, certain subsets of three of the two-body marginals suffice for the characterization. We also discuss generalizations of the statement to pure states of more particles, showing that these are almost always determined among pure states by three of their $(n-2)$-body marginals. Finally, we present special families of symmetric pure four-particle states that share the same two-body marginals and are therefore undetermined. These are four-qubit Dicke states in superposition with generalized GHZ states.