The maximally entangled symmetric state in terms of the geometric measure

Abstract

The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which maps an n qubit symmetric state to n points on the unit sphere. It is shown how symmetries of the point distribution can be exploited to simplify the calculation of entanglement and also help find the maximally entangled symmetric state. Using a combination of analytical and numerical results, the most entangled symmetric states for up to 12 qubits are explored and discussed. The optimization problem on the sphere presented here is then compared with two classical optimization problems on the S^2 sphere, namely Toth's problem and Thomson's problem, and it is observed that, in general, they are different problems.

18 pages, 15 figures, small corrections and additions to contents and references

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Cited by in corpus (13)

• Exploring pure quantum states with maximally mixed reductions
• Multiqubit symmetric states with maximally mixed one-qubit reductions
• Maximum nonlocality in the (3,2,2) scenario
• Decoherence Effects on the Non-locality of Symmetric States
• Anticoherence measures for pure spin states
• Nonlocality and Entanglement for Symmetric States
• Non equilibrium dissipation-driven steady many-body entanglement
• Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
• A brief introduction to multipartite entanglement
• Tensor eigenvalues and entanglement of symmetric states
• Limits to multipartite entanglement generation with bosons and fermions
• Local unitary group stabilizers and entanglement for multiqubit symmetric states
• Geometric measure of entanglement of symmetric d-qubits is polynomial-time computable