We present a set of conditions that an arbitrary pure tripartite state must satisfy in order that the Entanglement of Formation (EOF) becomes a monogamic measure. The monogamic relation derived is deeply connected to the discrepancy between classical and quantum correlations, embodying the possible negative signal of the EOF tangle whenever the quantum correlation is larger than the classical one. The estimated limits bound the possible amount of quantum conditional entropy in the system. We present general analytical results for a three- qubit system and give a simple numerical algorithm to calculate the EOF tangle for a system with dimension 2 × 2 × N. Those results are employed to elucidate features of the distribution of entanglement during a dynamical evolution. See more athttp://xxx.lanl.gov/abs/1110.1054

Quantum discord (QD) measures the fraction of the pairwise mutual information that is locally inaccessible, in a multipartite system. Fundamental aspects related to two important measures in quantum information theory the Entanglement of Formation (EOF) and the conditional entropy, can be understood in terms of the distribution of this form of Local Inaccessible Information (LII). As such, the EOF for an arbitrarily mixed bipartite system AB can be related to the gain or loss of LII due to the extra knowledge that a purifying ancillary system E has on the pair AB. Similarly, a clear meaning of the negativity of the conditional entropy for AB is given. We exemplify by showing that these relations elucidate important and yet not well understood quantum features, such as the bipartite entanglement sudden death and the distinction between EOF and QD for quantifying quantum correlation. For that we introduce the concept of LII flow which quantifies the LII shared in multipartite system when a sequential local measurements are performed. To appear in New Journal of Physics. See preprint athttp://xxx.lanl.gov/abs/1106.0289

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