Quantum computation and quantum information
Quantum computation and quantum information
Geometric entanglement of symmetric states and the majorana representation
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
An introduction to entanglement measures
Quantum Information & Computation
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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.