SU(2) Invariants of Symmetric Qubit States

TL;DR

This paper explores the invariants of symmetric N-qubit states using the multiaxial representation, providing explicit calculations for spin-1 states and connecting density matrices with Fano parameters.

Contribution

It introduces a method to enumerate and explicitly calculate SU(2) invariants of symmetric qubit states using axes and scalars in the multiaxial representation.

Findings

Number of invariants characterized by axes and scalars

Explicit invariants calculated for pure and mixed spin-1 states

Connection between density matrix parameters and invariants

Abstract

Density matrix for N-qubit symmetric state or spin-j state (j = N/2) is expressed in terms of the well known Fano statistical tensor parameters. Employing the multiaxial representation [1], wherein a spin-j density matrix is shown to be characterized by j(2j+1) axes and 2j real scalars, we enumerate the number of invariants constructed out of these axes and scalars. These invariants are explicitly calculated in the particular case of pure as well as mixed spin-1 state.