Experimental Validation of Quantum Steering Ellipsoids and Tests of Volume Monogamy Relations
Chao Zhang, Shuming Cheng, Li Li, Qiuyue Liang, Bi‐Heng Liu, Yun‐Feng Huang, Chuan‐Feng Li, Guang‐Can Guo, Michael J. W. Hall, Howard M. Wiseman, Geoff J. Pryde · Physical Review Letters · 2019
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 characterization of the initial two-qubit state, and various aspects of entanglement are reflected in its geometric properties. We experimentally verify these properties via measurements on many different polarization-entangled photonic qubit states. Moreover, for pure three-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 polarization 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.