  Quantum entanglement and nonlocality are inequivalent notions: There exist
entangled states that nevertheless admit local-realistic interpretations. This
paper studies a special class of local-hidden-variable theories, in which the
linear structure of quantum measurement operators is preserved. It has been
proven that a quantum state has such linear hidden-variable representations if,
and only if, it is not entangled. Separable states are known to admit
nonclassical correlations as well, which are captured by quantum discord and
related measures. In the unified framework presented in this paper,
zero-discordant states are characterized as the only states that admit fully
consistent classical probability representations. Possible generalization of
this framework to the quasiprobability representation of multipartite quantum
states is also discussed.
