Wang Zizhu, Singh Sukhwinder, Navascués Miguel
Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria.
Phys Rev Lett. 2017 Jun 9;118(23):230401. doi: 10.1103/PhysRevLett.118.230401. Epub 2017 Jun 8.
We consider the problem of detecting entanglement and nonlocality in one-dimensional (1D) infinite, translation-invariant (TI) systems when just near-neighbor information is available. This issue is deeper than one might think a priori, since, as we show, there exist instances of local separable states (classical boxes) which admit only entangled (nonclassical) TI extensions. We provide a simple characterization of the set of local states of multiseparable TI spin chains and construct a family of linear witnesses which can detect entanglement in infinite TI states from the nearest-neighbor reduced density matrix. Similarly, we prove that the set of classical TI boxes forms a polytope and devise a general procedure to generate all Bell inequalities which characterize it. Using an algorithm based on matrix product states, we show how some of them can be violated by distant parties conducting identical measurements on an infinite TI quantum state. All our results can be easily adapted to detect entanglement and nonlocality in large (finite, not TI) 1D condensed matter systems.
我们考虑在仅可获得近邻信息的情况下，检测一维（1D）无限平移不变（TI）系统中的纠缠和非定域性问题。这个问题比人们先验认为的要深刻，因为正如我们所展示的，存在仅允许纠缠（非经典）TI扩展的局域可分态（经典盒）实例。我们给出了多可分TI自旋链局域态集合的简单特征描述，并构造了一族线性见证，其可从最近邻约化密度矩阵检测无限TI态中的纠缠。类似地，我们证明经典TI盒的集合构成一个多面体，并设计了一个生成所有刻画它的贝尔不等式的通用程序。使用基于矩阵乘积态的算法，我们展示了在对无限TI量子态进行相同测量时，远处的参与方如何能违背其中一些不等式。我们所有的结果都可以很容易地适用于检测大型（有限，非TI）1D凝聚态物质系统中的纠缠和非定域性。
