Experimental Observation of Hierarchy in Temporal Quantum Correlations

The concepts of entanglement (or inseparability), steering, and Bell nonlocality form a logical hierarchy as manifested by the strict hierarchy of the entangled states, steerable states, and Bell-nonlocal states as well as the securities of the standard quantum key distribution (QKD), one-sided device-independent QKD, and device-independent QKD. In this work, we report the experimental observation of the hierarchy in their temporal analogues-- the temporal inseparability, temporal steering, and temporal CHSH inequality (or nonmacrorealism). These temporal quantum correlations, which quantify the two-time correlation of a quantum state with characterized or uncharacterized measurements, can exhibit distinct dynamics in quantum channels as a consequence of the hierarchy. Using the superconducting qubits provided by the IBM Quantum Experience, we observe the signature of the hierarchy in a depolarizing quantum channel while investigating the sudden death of these temporal quantum correlations. In addition, we also study how one may use these temporal quantum correlations to signify the non-Markovianity and benchmark the security of QKD.