DAMPT, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Inria and Université Paris Diderot, LIAFA, Case 7014, 75205 Paris Cedex 13, France.
Phys Rev Lett. 2015 Sep 18;115(12):120404. doi: 10.1103/PhysRevLett.115.120404.
The results of spacelike separated measurements are independent of distant measurement settings, a property one might call two-way no-signaling. In contrast, timelike separated measurements are only one-way no-signaling since the past is independent of the future but not vice versa. For this reason some temporal correlations that are formally identical to nonclassical spatial correlations can still be modeled classically. We propose a new formulation of Bell's theorem for temporal correlations; namely, we define nonclassical temporal correlations as the ones which cannot be simulated by propagating in time the classical information content of a quantum system given by the Holevo bound. We first show that temporal correlations between results of any projective quantum measurements on a qubit can be simulated classically. Then we present a sequence of general measurements on a single m-level quantum system that cannot be explained by propagating in time an m-level classical system and using classical computers with unlimited memory.
时空间隔的测量结果彼此独立，与远处的测量设置无关，这一性质可称为双向无信号。相反，类时间隔的测量只有单向无信号，因为过去独立于未来，但反之则不然。由于这个原因，一些在形式上与非经典空间相关相同的时间相关仍然可以用经典模型来描述。我们提出了一种新的用于时间相关的贝尔定理表述；也就是说，我们将非经典时间相关定义为那些不能通过在时间上传播量子系统的经典信息量来模拟的相关，这个信息量由 Holevo 界限给出。我们首先证明，对单量子比特上的任何投影量子测量结果之间的时间相关可以用经典方法来模拟。然后，我们提出了一系列对单个 m 能级量子系统的一般测量，这些测量不能通过在时间上传播 m 能级经典系统并使用具有无限内存的经典计算机来解释。
