Majorana representation of symmetric multiqubit states

TL;DR

This paper reviews the Majorana representation of symmetric multiqubit states, highlighting its role in classifying entanglement, analyzing correlation structures, and evaluating geometric entanglement measures in quantum information science.

Contribution

It provides a comprehensive overview of the Majorana representation's application to symmetric states and introduces simplified methods for entanglement analysis.

Findings

Classification of entanglement families based on Majorana spinors

Development of a simplified method to evaluate geometric entanglement

Insights into how correlation information is imprinted in symmetric states

Abstract

As early as 1932, Majorana had proposed that a pure permutation symmetric state of N spin- 1 2 particles can be represented by N spinors, which correspond geometrically to N points on the Bloch sphere. Several decades after its conception, the Majorana representation has recently attracted a great deal of attention in connection with multiparticle entanglement. A novel use of this represen- tation led to the classification of entanglement families of permutation symmetric qubits - based on the number of distinct spinors and their arrangement in constituting the multiqubit state. An elegant approach to explore how correlation information of the whole pure symmetric state gets imprinted in its parts is developed for specific entanglement classes of symmetric states. More- over, an elegant and simplified method to evaluate geometric measure of entanglement in N-qubit states obeying exchange symmetry has been developed based on the distribution of the constituent Majorana spionors over the unit sphere. Multiparticle entanglement being a key resource in sev- eral quantum information processing tasks, its deeper understanding is essential. In this review, we present a detailed description of the Majorana representation of pure symmetric states and its applicability in investigating various aspects of multiparticle entanglement.