Canonical steering ellipsoids of pure symmetric multiqubit states with two distinct spinors and volume monogamy of steering

Quantum steering ellipsoid formalism provides a faithful representation of all two-qubit states and is useful for obtaining their correlation properties. The steering ellipsoids of two-qubit states that have undergone local operations on both the qubits, in order to bring the state to its canonical form, are the so-called canonical steering ellipsoids. The steering ellipsoids corresponding to the two-qubit subsystems of permutation-symmetric N-qubit states are considered here. We construct and analyze the geometric features of the canonical steering ellipsoids corresponding to pure permutation-symmetric N-qubit states with two distinct spinors. Depending on the degeneracy of the two spinors in the pure symmetric N-qubit state, several families arise which cannot be converted into one another through stochastic local operations and classical communication (SLOCC). The canonical steering ellipsoids of the two-qubit states drawn from the pure symmetric N-qubit states with two distinct spinors allow for a geometric visualization of the SLOCC-equivalent class of states. We show that the states belonging to the W class correspond to oblate spheroids centered at (0, 0, 1/(N - 1)) with fixed semiaxis lengths 1/root N - 1 and 1/(N - 1). The states belonging to all other SLOCC-inequivalent families correspond to ellipsoids centered at the origin of the Bloch sphere. We also explore volume monogamy relations of states belonging to these families, mainly the W class of states.

Automated summary

The quantum steering ellipsoid formalism accurately represents two-qubit states and is useful for studying their correlation properties. This study focuses on the steering ellipsoids of permutation-symmetric N-qubit states. The geometry of the canonical steering ellipsoids of pure permutation-symmetric N-qubit states with two distinct spinors is analyzed, revealing several families that cannot be converted into each other through stochastic local operations and classical communication. These families allow for a geometric visualization of the SLOCC-equivalent class of states.