Detecting breaking channels without entanglement

Huan-Yu Ku^1,2*, Shin-Liang Chen^1,3, Wenbin Zhou⁴, Neill Lambert², Franco Nori^2,5, Yueh-Nan Chen^1,2

¹Department of Physics and Center for Quantum Frontiers of Research Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan
²Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
³Dahlem Center for Complex Quantum Systems, Free University Berlin, Berlin, Germany
⁴Graduate School of Informatics, Nagoya University, Chikusa-ku, 464-8601 Nagoya, Japan
⁵Department of Physics, The University of Michigan, Ann Arbor, 48109-1040 Michigan, USA

* Presenter:Huan-Yu Ku, email:huan_yu@phys.ncku.edu.tw

Quantum channels breaking the entanglement, incompatibility, and nonlocality are respectively useless for the entanglement based, one-sided device-independent, and device-independent quantum information processing. Here, we show that the above breaking channels relate with the temporal quantum correlations e.g., temporal separability, channel unsteerability, temporal unsteerability, and macrorealism. More specifically, we first define the steerability breaking channel, which is similar to the entanglement and nonlocality breaking channels, and show the steerability breaking channel is identical to the incompatibility breaking the channel. We prove that the measure of the temporal nonseparability is a memory monotone under the framework of the resource theory of the quantum memory with an additional assumption. The steerability breaking channel can be certified with the channel steering. We also show that the temporal steerability and the macrorealism can witness the steerability breaking and the nonlocality breaking the unital channel. As an explicit example, a 2-dimensional depolarizing channel is considered to compare the temporal quantum correlations with the breaking channels.
Similar to the hierarchy relations with the temporal and spatial quantum correlations, the hierarchy with the breaking channels is discussed.

Keywords: Quantum network, Quantum communication, Quantum memory, temporal quantum correaltion