Canonical steering ellipsoids of pure symmetric multiqubit states with two distinct spinors and volume monogamy of steering
B. G. Divyamani, I. Reena, Prasanta Kumar Panigrahi, A. R. Usha Devi, Sudha · Physical Review A · 2023
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 $(0,0,1/(N\ensuremath{-}1))$ with fixed semiaxis lengths $1/\sqrt{N\ensuremath{-}1}$ and $1/(N\ensuremath{-}1)$. 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.