Interconvertibility and irreducibility of permutation symmetric three qubit pure states

TL;DR

This paper uses Majorana geometric representation to analyze entanglement classes of permutation symmetric three-qubit states, revealing differences in irreducibility and interconvertibility among key states like W and GHZ.

Contribution

It introduces a novel Majorana-based framework to distinguish entanglement families and demonstrates how certain states' correlations are embedded in their reduced states.

Findings

GHZ state has irreducible correlations that cannot be inferred from parts.

W state’s correlation information is fully contained in its two-party reduced states.

Contrasting irreducibility features of interconvertible states are elucidated.

Abstract

A novel use of Majorana geometric representation brings out distinct entanglement families of permutation symmetric states of qubits. The paradigmatic W and GHZ (Greenberger-Horne-Zeilinger) states of three qubits respectively contain two and three independent Majorana spinors. Another unique state with three distinct Majorana spinors -- constructed through a permutation symmetric superposition of two up qubits and one down qubit (W state) and its obverse state Wbar) exhibits genuine three-party entanglement, which is robust under loss of a qubit. While the GHZ state has irreducible correlations and cannot be determined from its parts, we show here that the correlation information of the W-superposition state is imprinted uniquely in its two party reduced states. This striking example sheds light on the contrasting irreducibility features of interconvertible states.