Ent: A Multipartite Entanglement Measure, and Parameterization of Entangled States

TL;DR

This paper introduces a new multipartite entanglement measure called the ent, proves its properties, and develops methods for constructing maximally entangled states and a multipartite Schmidt decomposition.

Contribution

It presents the ent as a normalized entanglement monotone, constructs maximally entangled states, and proposes a multipartite Schmidt decomposition for pure states.

Findings

The ent is an entanglement monotone with automatic normalization.

Maximally entangled states and bases are constructed for all multipartite systems.

A multipartite Schmidt decomposition and a general entanglement measure for mixed states are developed.

Abstract

A multipartite entanglement measure called the ent is presented and shown to be an entanglement monotone, with the special property of automatic normalization. Necessary and sufficient conditions are developed for constructing maximally entangled states in every multipartite system such that they are true-generalized X states (TGX) states, a generalization of the Bell states, and are extended to general nonTGX states as well. These results are then used to prove the existence of maximally entangled basis (MEB) sets in all systems. A parameterization of general pure states of all ent values is given, and proposed as a multipartite Schmidt decomposition. Finally, we develop an ent vector and ent array to handle more general definitions of multipartite entanglement, and the ent is extended to general mixed states, providing a general multipartite entanglement measure.