How not to Renyi generalize the Quantum Conditional Mutual Information

We study the relation between the quantum conditional mutual information and the quantum $alpha$-Renyi divergences. Considering the totally antisymmetric state we show that it is not possible to attain a proper generalization of the quantum conditional mutual information by optimizing the distance in terms of quantum $alpha$-Renyi divergences over the set of all Markov states. The failure of the approach considered arises from the observation that a small quantum conditional mutual information does not imply that the state is close to a quantum Markov state.

Experimentally feasible set of criteria detecting genuine multipartite entanglement in n-qubit Dicke states and in higher dimensional systems

We construct a set of criteria detecting genuine multipartite entanglement in arbitrary dimensional multipartite systems. These criteria are optimally suited for detecting multipartite entanglement in n-qubit Dicke states with m-excitations. In a detailed analysis we show that the criteria are also more robust to noise than any other criterion known so far, especially with increasing system size. Furthermore it is shown that the number of required local observables scales only polynomially with size, thus making the criteria experimentally feasible.