# Majorana representation of symmetric multiqubit states

Majorana representation of symmetric multiqubit states As early as 1932, Majorana had proposed that a pure permutation symmetric state of N spin- $${\frac{1}{2}}$$ 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 representation 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. Moreover, 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 several 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Majorana representation of symmetric multiqubit states

, Volume 11 (3) – Aug 27, 2011
26 pages

/lp/springer_journal/majorana-representation-of-symmetric-multiqubit-states-APP3DMhg03
Publisher
Springer Journals
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematics, general; Quantum Physics; Physics, general; Computer Science, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0280-8
Publisher site
See Article on Publisher Site

### Abstract

As early as 1932, Majorana had proposed that a pure permutation symmetric state of N spin- $${\frac{1}{2}}$$ 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 representation 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. Moreover, 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 several 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.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 27, 2011

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