Hierarchy of Efficiently Computable and Faithful Lower Bounds to Quantum Discord.

Quantum discord expresses a fundamental nonclassicality of correlations that is more general than entanglement, but that, in its standard definition, is not easily evaluated. We derive a hierarchy of computationally efficient lower bounds to the standard quantum discord. Every nontrivial element of the hierarchy constitutes by itself a valid discordlike measure, based on a fundamental feature of quantum correlations: their lack of shareability. Our approach emphasizes how the difference between entanglement and discord depends on whether shareability is intended as a static property or as a dynamical process.