Experimental verification of the steering ellipsoid zoo via two-qubit states

TL;DR

This paper experimentally verifies the quantum steering ellipsoid zoo using two-qubit photonic states, demonstrating its effectiveness in characterizing entanglement, steering, and discord through geometric properties.

Contribution

It provides the first experimental validation of the quantum steering ellipsoid zoo and shows how to reconstruct ellipsoids from measurement directions, advancing quantum state characterization.

Findings

Verified various quantum ellipsoids with high-fidelity two-qubit states.

Certified entanglement, EPR steering, and discord via geometric properties.

Reconstructed steering ellipsoids using icosahedron vertices as measurement directions.

Abstract

Quantum steering ellipsoid visualizes the set of all qubit states that can be steered by measuring on another correlated qubit in the Bloch picture. Together with local reduced states, it provides a faithful geometric characterization of the underlying two-qubit state so that almost all nonclassical state features can be reflected in its geometric properties. Consequently, the various types of quantum ellipsoids with different geometric properties form an ellipsoid zoo, which, in this work, is experimentally verified via measurements on many polarization-path photonic states. By generating two-qubit states with high fidelity, the corresponding ellipsoids are constructed to certify the presence of entanglement, one-way Einstein-Podolsky-Rosen steering, discord, and steering incompleteness. It is also experimentally verified that the steering ellipsoid can be reconstructed from using the twelve vertices of the icosahedron as measurement directions. Our results aid progress in applying the quantum steering ellipsoid to reveal nonclassical features of the multi-qubit system.