Entanglement, detection, and geometry of nonclassical states

Nonclassical states that are characterized by their nonpositive quasiprobabilities in phase space are known to be the basis for various quantum effects. In this work, we investigate the interrelation between the nonclassicality and entanglement, and then characterize the nonclassicality that precisely corresponds to entanglement. The results naturally follow from two findings: one is the general structure among nonclassical, entangled, separable, and classical states over Hermitian operators, and the other a general scheme to detect nonclassical states.