Deterministic Transformations of Multipartite Entangled States with Tensor Rank 2

TL;DR

This paper characterizes deterministic local transformations between multipartite entangled states of tensor rank 2, providing necessary and sufficient conditions, explicit transformation chains, and identifying invariant classes distinguished by a single parameter.

Contribution

It offers a complete set of criteria and explicit procedures for deterministic transformations of multipartite rank-2 entangled states, a previously unresolved problem.

Findings

Necessary and sufficient conditions for transformations

Transformation chains with at most one local operation per party

Invariant classes characterized by a single real parameter

Abstract

Transformations involving only local operations assisted with classical communication are investigated for multipartite entangled pure states having tensor rank 2. All necessary and sufficient conditions for the possibility of deterministically converting truly multipartite, rank-2 states into each other are given. Furthermore, a chain of local operations that successfully achieves the transformation has been identified for all allowed transformations. The identified chains have two nice features: (1) each party needs to carry out at most one local operation and (2) all of these local operations are also deterministic transformations by themselves. Finally, it is found that there are disjoint classes of states, all of which can be identified by a single real parameter, which remain invariant under deterministic transformations.