Correlance and discordance: computable measures of nonlocal correlation

Abstract

We present six new measures of nonlocal correlation for discrete multipartite quantum systems; correlance, statance, probablance, strong discordance, discordance, and diagonal discordance. The correlance measures all nonlocal correlations (even bound entanglement) and is exactly computable for all pure and mixed states. Statance and probablance are not yet computable, but motivate the strong discordance (for nonlocal correlation beyond that achievable by a strictly classical state), discordance (a measure of all nonlocal correlation in distinguishably quantum states), and diagonal discordance (for nonlocal correlation in diagonal states), all of which are exactly computable for all states. We discuss types of correlation and notions of classicality and compare correlance, strong discordance, and discordance to quantum discord. We also define diagonal correlance to handle strictly classical probability distributions, providing a powerful tool with wide-ranging applications.