Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland.
Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland.
Phys Rev Lett. 2015 Mar 13;114(10):100402. doi: 10.1103/PhysRevLett.114.100402. Epub 2015 Mar 10.
Bell's theorem applies to the normalizable approximations of original Einstein-Podolsky-Rosen (EPR) state. The constructions of the proof require measurements difficult to perform, and dichotomic observables. By noticing the fact that the four mode squeezed vacuum state produced in type II down-conversion can be seen both as two copies of approximate EPR states, and also as a kind of polarization supersinglet, we show a straightforward way to test violations of the EPR concepts with direct use of their state. The observables involved are simply photon numbers at outputs of polarizing beam splitters. Suitable chained Bell inequalities are based on the geometric concept of distance. For a few settings they are potentially a new tool for quantum information applications, involving observables of a nondichotomic nature, and thus of higher informational capacity. In the limit of infinitely many settings we get a Greenberger-Horne-Zeilinger-type contradiction: EPR reasoning points to a correlation, while quantum prediction is an anticorrelation. Violations of the inequalities are fully resistant to multipair emissions in Bell experiments using parametric down-conversion sources.
贝尔定理适用于原始爱因斯坦-波多尔斯基-罗森（EPR）态的可归一化近似。证明的构造需要难以执行的测量和二分可观测量。通过注意到在 II 型下转换中产生的四模压缩真空态既可以看作是两个近似 EPR 态的副本，也可以看作是一种极化超单态，我们展示了一种直接使用其态来测试 EPR 概念违反的简单方法。所涉及的可观测量只是偏振分束器输出处的光子数。合适的连锁贝尔不等式基于距离的几何概念。对于一些设置，它们可能是量子信息应用的新工具，涉及非二分性的可观测量，因此具有更高的信息容量。在无穷多设置的极限下，我们得到了一个格林伯格-霍恩-泽林格类型的矛盾：EPR 推理指向相关性，而量子预测是反相关性。在使用参量下转换源的贝尔实验中，不等式的违反完全抵抗多对发射。
