Duan Runyao, Feng Yuan, Ji Zhengfeng, Ying Mingsheng
State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, China, 100084.
Phys Rev Lett. 2007 Jun 8;98(23):230502. doi: 10.1103/PhysRevLett.98.230502. Epub 2007 Jun 4.
We show that an arbitrary basis of a multipartite quantum state space consisting of K distant parties such that the kth party has local dimension dk always contains at least N= Sigma(k=1)(K) (dk-1)+1 members that are unambiguously distinguishable using local operations and classical communication (LOCC). We further show that this lower bound is optimal by analytically constructing a special product basis having only N members unambiguously distinguishable by LOCC. Interestingly, such a special product basis not only gives a stronger form of the weird phenomenon "nonlocality without entanglement," but also implies the existence of a locally distinguishable entangled basis.
我们证明，由K个相距遥远的方组成的多体量子态空间的任意一个基，其中第k个方具有局部维度dk，总是包含至少N = Σ(k = 1)(K) (dk - 1) + 1个成员，这些成员可通过局部操作和经典通信（LOCC）明确区分。我们进一步通过解析构造一个特殊的积基来表明这个下界是最优的，该积基只有N个成员可通过LOCC明确区分。有趣的是，这样一个特殊的积基不仅给出了“无纠缠的非局域性”这种奇特现象的更强形式，还意味着存在一个局部可区分的纠缠基。
