Quantum Correlations in Classical Statistics

A. K. Rajagopal, R. W. Rendell

A density-matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical underpinning of these correlations. As a by-product of this analysis, a physical basis of the classical statistical correlations leading to additive entropy in a bipartite system discussed recently by Tsallis emerges as inherent classical spin fluctuations. It is found that in this example, the quantum correlations shrink the region of additivity in phase space.

Andrei Yu. Khrennikov

K. Bruce Winterbon

Junwei Zhang, Ruifang He, Li Zhao +4 more

In machine learning, classification algorithms often use statistical methods to build the correspondence between features (or attributes) and categories (or labels), that is, the statistical correlation between features and categories. In quantum theory, a large number of experimental results show that quantum correlation is far stronger than what can be explained by local hidden theory (i.e., classical or non-quantum theory), that is, quantum mechanics theory reveals a statistical correlation stronger than that described by classical theory. Based on this, this paper will use the strong statistical correlation revealed by Bell state to build a classification algorithm to verify the validity and superiority of the formal framework of quantum mechanics in specific classification tasks. Specifically, we use quantum joint probabilities derived from the measurement process of Bell state to model the quantum statistical correlation between features and categories. The paper first theoretically proves that the formal framework used has the ability to violate Bell inequality; moreover, a classification algorithm is implemented and verified on classic machine learning datasets. Experimental results show that the algorithm is significantly better than most mainstream machine learning algorithms.

Klavs Hansen

Jan Sperling, Tim J. Bartley, Gaia Donati +5 more

We study, in theory and experiment, the quantum properties of correlated light fields measured with click-counting detectors providing incomplete information on the photon statistics. We establish a correlation parameter for the conditional statistics, and we derive the corresponding nonclassicality criteria for detecting conditional quantum correlations. Classical bounds for Pearson's correlation parameter are formulated that allow us, once they are violated, to determine nonclassical correlations via the joint statistics. On the one hand, we demonstrate nonclassical correlations in terms of the joint click statistics of light produced by a parametric down-conversion source. On the other hand, we verify quantum correlations of a heralded, split single-photon state via the conditional click statistics together with a generalization to higher-order moments. We discuss the performance of the presented nonclassicality criteria to successfully discern joint and conditional quantum correlations. Remarkably, our results are obtained without making any assumptions on the response function, quantum efficiency, and dark-count rate of photodetectors.