Coarse-grained entanglement classification through orthogonal arrays

TL;DR

This paper introduces a new coarse-grained method for classifying entanglement in multipartite quantum systems using orthogonal arrays, extending analysis beyond bipartite and small qubit systems.

Contribution

It proposes a novel entanglement classification framework based on orthogonal arrays applicable to systems with arbitrary levels and sizes, including highly entangled states and MDS codes.

Findings

Analyzed four- and five-qubit systems.

Extended classification to heterogeneous tripartite systems.

Identified properties of states related to maximum distance separable codes.

Abstract

Classification of entanglement in multipartite quantum systems is an open problem solved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in systems consisting of $N$ subsystems with an arbitrary number of internal levels each, based on properties of orthogonal arrays with $N$ columns. In particular, we investigate in detail a subset of highly entangled pure states which contains all states defining maximum distance separable codes. To illustrate the methods presented, we analyze systems of four and five qubits, as well as heterogeneous tripartite systems consisting of two qubits and one qutrit or one qubit and two qutrits.