Entanglement transitivity in multipartite systems
Gelo Noel Tabia1,2*, Chung-Yun Hsieh3, Kai-Siang Chen2, Yu-Chun Yin2, Yeong-Cherng Liang2
1Center for Quantum Technology, National Tsing Hua University, Hsinchu 300, Taiwan
2Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan
3ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain
* Presenter:Gelo Noel Tabia, email:gelo.tabia@gmail.com
One of the major goals in scientific inquiry is to understand the relation between a whole and its parts. In quantum information, this is manifest in the problem of detecting genuine multipartite entanglement from knowledge of some reduced states. In this work, we focus on a different but related question: can marginal information reveal new marginal information? For instance, it can be shown that there are sets of entangled marginal states for a joint multipartite state that imply that a certain unknown marginal state must also be entangled. We call this the transitivity of entanglement. We use the Peres-Horodecki criterion to formulate a semidefinite program that can certify the entanglement transitivity in a target bipartite system. We also consider an extension of the problem to cases where some of the known marginal states are separable, which we call metatransitivity. We demonstrate that metatransitivity in the tripartite setting can be obtained from qudit Werner and isotropic states. Finally we discuss a potential application and some future directions that go beyond entanglement.

Keywords: multipartite entanglement, transitivity, marginal information