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Locally distinguishing multipartite orthogonal product states with different entanglement resource
Quantum Information Processing ( IF 2.5 ) Pub Date : 2021-02-19 , DOI: 10.1007/s11128-021-03016-0
Zhi-Chao Zhang , Qing-Le Wang

Recently, entanglement-assisted state discrimination has attracted much attention. However, most of the relevant results are about the bipartite quantum states and very little is known about the multipartite case. In this paper, considering the nonlocal orthogonal product states constructed by Jiang and Xu [Phys. Rev. A 102, 032211 (2020)], we first present one protocol to locally distinguish a set of orthogonal product states in \(3\otimes 3 \otimes 3\) by using a \(2\otimes 2\) maximally entangled state. Then, we generalize the distinguishing method for the class of nonlocal of orthogonal product states in \(\otimes _{j=1}^n{\mathbb {C}}^{d_j}\), where \(n\geqslant 3, d_j\geqslant 2, j=1,2,\ldots ,n\). Furthermore, for another class of orthogonal product states in \(\otimes _{j=1}^n{\mathbb {C}}^{d_j}\), where \(n\geqslant 3, d_j\geqslant 3, j=1,2,\ldots ,n\), we prove that these states can also be distinguished by LOCC with a \(3\otimes 3\) maximally entangled state or two copies of \(2\otimes 2\) maximally entangled states. The above results can let us better understand how to use entanglement resource more efficiently in multipartite quantum systems and also reveal the phenomenon of less nonlocality with more entanglement.



中文翻译:

具有不同纠缠资源的局部区分多产品正交产品状态

近年来,纠缠态的国家歧视引起了人们的广泛关注。但是,大多数相关结果与二分量子态有关,而对多分情形的了解却很少。在本文中,考虑了由江和徐[物理物理学报,2000年 修订版A 102,032211(2020)],我们首先呈现一个协议,以在本地区分一组正交产品状态\(3 \ otimes 3 \ otimes 3 \)通过使用\(2 \ otimes 2 \)最大纠缠状态。然后,我们归纳出\(\ otimes _ {j = 1} ^ n {\ mathbb {C}} ^ {d_j} \)中的正交乘积状态的非局部类的区分方法,其中\(n \ geqslant 3 ,d_j \ geqslant 2,j = 1,2,\ ldots,n \)。此外,对于\(\ otimes _ {j = 1} ^ n {\ mathbb {C}} ^ {d_j} \)中的另一类正交乘积状态,其中\(n \ geqslant 3,d_j \ geqslant 3,j = 1,2,\ ldots,n \),我们证明了这些状态也可以通过LOCC与\(3 \ otimes 3 \)最大纠缠态或\(2 \ otimes 2 \)最大纠缠态的两个副本加以区分。状态。上述结果可以使我们更好地理解如何在多粒子量子系统中更有效地利用纠缠资源,并且还揭示了纠缠度更高,非局部性较小的现象。

更新日期:2021-02-19
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