Experimental validation of quantum steering ellipsoids and tests of volume monogamy relations

TL;DR

This paper experimentally verifies the geometric properties of quantum steering ellipsoids in photonic qubits and tests volume monogamy relations, revealing their validity and limitations in pure and mixed states.

Contribution

It provides the first experimental validation of the geometric properties of quantum steering ellipsoids and tests the volume monogamy relations in three-qubit states.

Findings

Quantum steering ellipsoids accurately characterize 2-qubit states.

Pure 3-qubit states satisfy a strong volume monogamy relation.

Mixed entangled states can violate the strong monogamy but satisfy a weaker one.

Abstract

The set of all qubit states that can be steered to by measurements on a correlated qubit is predicted to form an ellipsoid---called the quantum steering ellipsoid---in the Bloch ball. This ellipsoid provides a simple visual characterisation of the initial 2-qubit state, and various aspects of entanglement are reflected in its geometric properties. We experimentally verify these properties via measurements on many different polarisation-entangled photonic qubit states. Moreover, for pure 3-qubit states, the volumes of the two quantum steering ellipsoids generated by measurements on the first qubit are predicted to satisfy a tight monogamy relation, which is strictly stronger than the well-known monogamy of entanglement for concurrence. We experimentally verify these predictions, using polarisation and path entanglement. We also show experimentally that this monogamy relation can be violated by a mixed entangled state, which nevertheless satisfies a weaker monogamy relation.