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

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