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

Abstract

Quantum steering ellipsoid formalism provides a faithful representation of all two-qubit states and helps in obtaining correlation properties of the state through the steering ellipsoid. The steering ellipsoids corresponding to the two-qubit subsystems of permutation symmetric $N$-qubit states is analysed here. The steering ellipsoids of two-qubit states that have undergone local operations on both the qubits so as to bring the state to its canonical form are the so-called canonical steering ellipsoids. 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, there arise several families which cannot be converted into one another through Stochastic Local Operations and Classical Communications (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-inequivalent class of states. We show that the states belonging to the W-class correspond to oblate spheroid centered at $(0,0,1/(N-1))$ with fixed semiaxes lengths $1/\sqrt{N-1}$ 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.

arXiv comment13 pages, 13 figures; Revised version; Comments welcome

References in corpus (17)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Distributed Entanglement
• Is Entanglement Monogamous?
• Local filtering operations on two qubits
• Quantum Steering Ellipsoids
• Operational Families of Entanglement Classes for Symmetric $N$-Qubit States
• Security proof for cryptographic protocols based only on the monogamy of Bell's inequality violations
• Quantum steering ellipsoids, extremal physical states and monogamy
• Entanglement Equivalence of $N$-qubit Symmetric States
• Majorana representation of symmetric multiqubit states
• Quantum discord of two-qubit rank-two states
• Volume monogamy of quantum steering ellipsoids for multi-qubit systems
• Geometric picture of quantum discord for two-qubit quantum states
• Monogamy of quantum correlations in three qubit pure states using Rajagopal-Rendell (RR) quantum deficit
• Canonical forms of two-qubit states under local operations
• Spin squeezing in symmetric multiqubit states with two distinct Majorana spinors
• Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states

Cited by in corpus (4)

• Experimental verification of the steering ellipsoid zoo via two-qubit states
• Symmetric quantum states: a review of recent progress
• Entanglement and volume monogamy features of permutation symmetric N-qubit pure states with N-distinct spinors: GHZ and WWbar states
• Lorentz invariants of pure three-qubit states