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

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