An alternative representation for pure symmetric states of qubits and its applications to entanglement classification

Abstract

We prove that the vast majority of symmetric states of qubits can be decomposed in a unique way into a superposition of spin 1/2 coherent states. For the case of two qubits, the proposed decomposition reproduces the Schmidt decomposition and therefore, in the case of a higher number of qubits, can be considered as its generalization. We analyze the geometrical aspects of the proposed representation and its invariant properties under the action of local unitary and local invertible transformations. As an application, we identify the most general classes of entanglement and representative states for any number of qubits in a symmetric state.

A qubit "flip" on the equations (13), (14) has been corrected. Equations (20), (21) have been modified in accordance

References in corpus (8)

• Permutationally invariant quantum tomography
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• Multiqubit symmetric states with high geometric entanglement
• The maximally entangled symmetric state in terms of the geometric measure
• Permutationally invariant state reconstruction
• Optimal state for keeping reference frames aligned and the Platonic solids
• Quantum geometric phase in Majorana's stellar representation: Mapping onto a many-body Aharonov-Bohm phase
• Inert states of spin-S systems

Cited by in corpus (10)

• Geometry of spin coherent states
• Anticoherence of spin states with point group symmetries
• Characterization of symmetry-protected topological phases in polymerized models by trajectories of Majorana stars
• Three-Tangle of a General Three-Qubit State in the Representation of Majorana Stars
• Symmetric 3 Qubit State Invariants
• Generalized Weyl-Heisenberg algebra, qudit systems and entanglement measure of symmetric states via spin coherent states
• Orthonormal bases of extreme quantumness
• Coherent-State Approach for Majorana representation
• Majorana stellar representation for mixed-spin $(s,\frac{1}{2})$ systems
• Non-Gaussianity from superselection rules