Majorana representation of symmetric multiqubit 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.

17 pages, No figures

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Cited by in corpus (36)

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• Quantumness of spin-1 states
• Evolution of tripartite entangled states in a decohering environment and their experimental protection using dynamical decoupling
• Optimal quantum tomography of permutationally invariant qubits
• Geometric description of modular and weak values in discrete quantum systems using the Majorana representation
• Operational Entanglement Families of Symmetric Mixed N-Qubit States
• Majorana representation of adiabatic and superadiabatic processes in three-level systems
• Quantumness Beyond Entanglement: The Case of Symmetric States
• Majorana representation, qutrit Hilbert space and NMR implementation of qutrit gates
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• Canonical steering ellipsoids of pure symmetric multiqubit states with two distinct spinors and volume monogamy of steering
• Coherent-State Approach for Majorana representation
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• Characterizing nonlocality of pure symmetric three-qubit states
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• Geometric decomposition of geodesics and null phase curves using Majorana star representation
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• Stellar representation of extremal Wigner-negative spin states
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• Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems
• Invariant Vector and Majorana Star Representations of Qutrit States
• Entanglement and volume monogamy features of permutation symmetric N-qubit pure states with N-distinct spinors: GHZ and WWbar states
• Three-qubit W state tomography via full and marginal state reconstructions on ibm_osaka
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• Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group