Experimental Observation of Hierarchy in Temporal Quantum Correlations

Hao-Cheng Weng¹, Chen-Yeh Wei^1*, Huan-Yu Ku², Shin-Liang Chen^2,3, Yueh-Nan Chen², Chih-Sung Chuu¹

¹Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
²Department of Physics and Center for Quantum Frontiers of Research & Technology, National Cheng Kung University, Tainan, Taiwan
³Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Berlin, Germany

* Presenter:Chen-Yeh Wei, email:yaya6414@gmail.com

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.

Keywords: quantum key distribution, quantum computer, quantum gate, Bell inequality