Highly entangled multi-qubit states with simple algebraic structure

TL;DR

This paper introduces a new method for finding highly entangled multi-qubit states that also have simple algebraic structures, leading to the discovery of states with high entanglement and simpler forms than previously known.

Contribution

The paper proposes an alternative search scheme focusing on states with high entanglement and simple algebraic structure, successfully finding new states for 4 to 8 qubits.

Findings

Discovered a maximally entangled 6-qubit state with simpler algebraic structure.

Found high entanglement states with simple structure for 7 qubits.

Presented preliminary results for 8-qubit states.

Abstract

Recent works by Brown et al and Borras et al have explored numerical optimisation procedures to search for highly entangled multi-qubit states according to some computationally tractable entanglement measure. We present an alternative scheme based upon the idea of searching for states having not only high entanglement but also simple algebraic structure. We report results for 4, 5, 6, 7 and 8 qubits discovered by this approach, showing that many of such states do exist. In particular, we find a maximally entangled 6-qubit state with an algebraic structure simpler than the best results known so far. For the case of 7, we discover states with high, but not maximum, entanglement and simple structure, as well as other desirable properties. Some preliminary results are shown for the case of 8 qubits.