@article {1452, title = {Detecting Consistency of Overlapping Quantum Marginals by Separability}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/03/03}, pages = {032105}, abstract = { The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general, and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known $k$-symmetric extension criterion for separability. }, doi = {10.1103/PhysRevA.93.032105}, url = {http://arxiv.org/abs/1509.06591}, author = {Jianxin Chen and Zhengfeng Ji and Nengkun Yu and Bei Zeng} }