Sang-Gyun Youn, Seoul National University
In quantum information theory, group symmetries have played crucial roles in studying quantum states and quantum channels. There have been somewhat sporadic but lots of efforts to analyze PPT entanglement under symmetries. We suggest an abstract approach using group symmetries, which offers additional advantages on the Horodecki criterion. In this case, we need to investigate only a much smaller number of positive maps. Indeed, we apply this approach to exhibit two main applications to study PPT entanglement: (1) there is no PPT non-entanglement-breaking quantum channel generated by the identity map, transpose map, depolarizing map, and diagonalization map, (2) there is no A-BC PPT entanglement for a class tripartite invariant quantum states with unitary group symmetries. These conclusions resolve open questions raised in some recent papers. In particular, the latter conclusion provides a strong contrast to the fact that there exist PPT entangled tripartite Werner states.