Strong superadditivity and monogamy of the Renyi measure of entanglement

Employing the quantum R\'enyi $\alpha$-entropies as a measure of entanglement, we numerically find the violation of the strong superadditivity inequality for a system composed of four qubits and $\alpha>1$. This violation gets smaller as $\alpha\rightarrow 1$ and vanishes for $\alpha=1$ when the measure corresponds to the Entanglement of Formation (EoF). We show that the R\'enyi measure aways satisfies the standard monogamy of entanglement for $\alpha = 2$, and only violates a high order monogamy inequality, in the rare cases in which the strong superadditivity is also violated. The sates numerically found where the violation occurs have special symmetries where both inequalities are equivalent. We also show that every measure satisfing monogamy for high dimensional systems also satisfies the strong superadditivity inequality. For the case of R\'enyi measure, we provide strong numerical evidences that these two properties are equivalent.Comment: replaced with final published versio

Entanglement Irreversibility From Quantum Discord And Quantum Deficit.

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 entanglement 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 local operations and classical communication 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.10702050

Environment-induced anisotropy and the sensitivity of the radical pair mechanism in the avian compass

Several experiments over the years have shown that the Earth's magnetic field is essential for orientation in birds migration. The most promising explanation for this orientation is the photo-stimulated radical pair (RP) mechanism. In order to define a reference frame for the orientation task radicals must have an intrinsic anisotropy. We show that this kind of anisotropy, and consequently the entanglement in the model, are not necessary for the proper functioning of the compass. Classically correlated initial conditions for the RP, subjected to a fast decoherence process, are able to provide the anisotropy required. Even a dephasing environment can provide the necessary frame for the compass to work, and also implies fast decay of any quantum correlation in the system without damaging the orientation ability. This fact significantly expands the range of applicability of the RP mechanism providing more elements for experimental search.Comment: 7 pages, 6 figures. Replaced with final published versio