A, B, C of Three-Qubit Entanglement: Three Vectors to Control It All

TL;DR

This paper introduces a vector-based approach to control three-qubit entanglement, enabling analytical solutions for state transformations and entanglement manipulation with limited access to qubits.

Contribution

It presents a novel vector representation linked to SO(6) and SU(4) groups for controlling three-qubit entanglement analytically.

Findings

Analytical transformation between W-type and GHZ states.

Manipulation of bipartite concurrences and three-tangle.

Design of quaternionic operations for quantum states.

Abstract

In this paper we are focusing on entanglement control problem in a three-qubit system. We demonstrate that vector representation of entanglement, associated with SO(6) representation of SU(4) two-qubit group, can be used to solve various control problems analytically including (i) the transformation between a W-type states and GHZ state, and (ii) manipulating bipartite concurrences and three-tangle under a restricted access to only two qubits, and (iii) designing USp(4)-type quaternionic operations and quantum states.