Geometric discord and measurement-induced nonlocality for well known bound entangled states (Englisch)

Abstract We employ geometric discord and measurement induced nonlocality to quantify quantumness of some well-known bipartite bound entangled states, namely the two families of Horodecki’s ($$2\otimes 4, 3\otimes 3$$ and $$4\otimes 4$$ dimensional) bound entangled states and that of Bennett et al.’s in $$3\otimes 3$$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $$4\otimes 4$$ bound entangled state of Benatti et al. and the $$2\otimes 8$$ state having the same matrix representation (in computational basis) is same. Coincidently, the $$2m\otimes 2m$$ Werner and isotropic states also exhibit the same property, when seen as $$2\otimes 2m^2$$ dimensional states.