HIERARCHY OF CORRELATIONS VIA LÜDERS MEASUREMENTS

Abstract

The classification and quantification of correlations (classical and quantum) in composite quantum systems are of fundamental significance for quantum information processing. While the paradigm of separability versus entanglement has been intensively studied, the scenario of classicality versus quantumness, with focus on the quantum discord, has also attracted many recent interests. In this paper, pursuing further the latter scenario and exploiting the intrinsic structure of bipartite quantum states via local projective measurements, we introduce the notion of coherent dimension of correlations in terms of the Lüders measurements. The coherent dimension can alternatively be regarded as a generalization of the Schmidt number of a pure state. Furthermore, we propose some families of measures for correlations, which extend naturally both the quantum discord and the quantum mutual information (total correlations), and furthermore interpolate between them. These quantities reveal some hierarchial structures, and provide a more complete description, of both classical and quantum correlations in the quantum realm.