Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
Phys Rev Lett. 2012 Jun 29;108(26):260403. doi: 10.1103/PhysRevLett.108.260403. Epub 2012 Jun 27.
We consider two celebrated criteria for defining the nonclassicality of bipartite bosonic quantum systems, the first stemming from information theoretic concepts and the second from physical constraints on the quantum phase space. Consequently, two sets of allegedly classical states are singled out: (i) the set C composed of the so-called classical-classical (CC) states-separable states that are locally distinguishable and do not possess quantum discord; (ii) the set P of states endowed with a positive P representation (P-classical states)-mixtures of Glauber coherent states that, e.g., fail to show negativity of their Wigner function. By showing that C and P are almost disjoint, we prove that the two defining criteria are maximally inequivalent. Thus, the notions of classicality that they put forward are radically different. In particular, generic CC states show quantumness in their P representation, and vice versa, almost all P-classical states have positive quantum discord and, hence, are not CC. This inequivalence is further elucidated considering different applications of P-classical and CC states. Our results suggest that there are other quantum correlations in nature than those revealed by entanglement and quantum discord.
我们考虑了两个定义二分量玻色量子系统非经典性的著名判据，第一个判据源于信息论概念，第二个判据源于量子相空间的物理约束。因此，我们挑选出了两组据称是经典的态：（i）由所谓的经典-经典（CC）态组成的集合 C——可分离的态，它们在局域上可区分且不具有量子纠缠；（ii）具有正 P 表象（P 经典态）的态的集合 P——混合了 Glauber 相干态，例如，它们的 Wigner 函数不具有负性。通过证明 C 和 P 几乎不相交，我们证明了这两个定义判据是最大不等价的。因此，它们提出的经典概念是截然不同的。特别地，一般的 CC 态在其 P 表象中表现出量子性，反之亦然，几乎所有的 P 经典态都具有正的量子纠缠，因此不是 CC 态。通过考虑 P 经典态和 CC 态的不同应用，进一步阐明了这种不等价性。我们的结果表明，自然界中存在着除了纠缠和量子纠缠所揭示的其他量子相关性。
