**Strong superadditivity and monogamy of the Renyi measure of entanglement** - Marcos César de Oliveira

Employing quantum Rényi α-entropies as a measure of entanglement, we numerically find violation of the strong superadditivity inequality for a system composed of four qubits and α>1. This violation gets smaller as α goes to 1 and vanishes for α=1.
For α=2, we also show that the Rényi measure satisfies the standard monogamy of entanglement and that the violation of the strong superadditivity occurs very rarely but always simultaneous to the violation of a high order monogamy inequality. We thus conjecture that
strong superadditivity violation of this entanglement measure is necessary and sufficient for the high order monogamy relation violation.