Two distinct classes of bound entanglement: PPT-bound and `multi-particle'-bound

TL;DR

This paper introduces new classes of multipartite, multidimensional bound entangled states, distinguished by their PPT properties and multi-particle nature, with implications for entanglement distillation.

Contribution

It systematically constructs novel bound entangled states using Weyl operators and explores their properties, including a distillation protocol for certain cases.

Findings

States are bound entangled due to PPT or multi-particle reasons.

Constructed classes have geometry independent of particle number.

Demonstrated limited entanglement increase via distillation for d=3.

Abstract

We introduce systematically with the help of Weyl operators novel classes of multipartite and multidimensional states which are all bound entangled for arbitrary dimension. We find that the entanglement is bound due to different reasons: unlockable due to the multi--particle nature and some states are in addition bound due the fact being positive under partial transposition (PPT). By a general construction (W simplices) we obtain classes of states which have the same geometry concerning separability and entanglement independent of the number of involved particle pairs. Moreover, we introduce a distillation protocol and demonstrate for d=3 that for a certain set of states the entanglement can be increased only up to a certain amount.