We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation – quantum discord and one-way quantum deficit. We show that the entangle- ment of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under LOCC for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distillable secret key and the quantum discord. Phys. Rev. Lett. 107, 020502 (2011) , also in http://xxx.lanl.gov/abs/1007.0228