The MES of tripartite qutrit states and pure state separable transformations which are not possible via LOCC

TL;DR

This paper characterizes the Maximally Entangled Set for tripartite qutrit states, identifying states reachable via separable operations but not through LOCC, revealing new insights into quantum state transformations.

Contribution

It provides the first characterization of the MES for three qutrit states and identifies pure state transformations possible via SEP but impossible via LOCC.

Findings

Identified the MES for generic three qutrit states.

Discovered states reachable by SEP but not by LOCC.

First examples of pure state transformations via SEP but not LOCC.

Abstract

Entanglement is the resource to overcome the restriction of operations to Local Operations assisted by Classical Communication (LOCC). The Maximally Entangled Set (MES) of states is the minimal set of n-partite pure states with the property that any truly n-partite entangled pure state can be obtained deterministically via LOCC from some state in this set. Hence, this set contains the most useful states for applications. In this work we characterize the MES for generic three qutrit states. Moreover, we analyze which generic three qutrit states are reachable (and convertible) under LOCC transformations. To this end we study reachability via separable operations (SEP), a class of operations that is strictly larger than LOCC. Interestingly, we identify a family of pure states that can be obtained deterministically via SEP but not via LOCC. To our knowledge these are the first examples of transformations among pure states that can be implemented via SEP but not via LOCC.