Necessary and Sufficient Quantum Beneficial Condition of Remote State Preparation

Yuan-Sung Liu^1,2*, Shih-Hsuan Chen^1,2, Bing-Yuan Lee^1,2, Chan Hsu^1,2, Guang-Yin Chen³, Yueh-Nan Chen², Che-Ming Li^1,2,4

¹Department of Engineering Science, National Cheng Kung University, Tainan 70101, Taiwan
²Center for Quantum Frontiers of Research & Technology, National Cheng Kung University, Tainan 70101, Taiwan
³Department of Physics, National Chung Hsing University, Taichung 40227, Taiwan
⁴Center for Quantum Technology, National Tsing Hua University, Hsinchu 30013, Taiwan

* Presenter:Yuan-Sung Liu, email:peter15131118@gmail.com

Quantum effects often show phenomena that classical physics cannot explain, and tasks that can show quantum beneficial effects have attracted attention. The remote state preparation (RSP) shows the quantum helpful effect protocol, which plays a vital role in quantum information tasks. Due to the fundamental part of the RSP in quantum technology, appraising the performance of the RSP is an essential issue. Previous works have discussed the different scenarios for scoring RSP and the related resources behind it. However, the existing scoring methods need to optimize the RSP protocol, which requires the ability of quantum state tomography and may not be able to score RSP effectively in practical applications such as quantum networking. To tackle this problem, we propose a new method to evaluate the RSP task, which faithfully describes the characteristics of the resource state and shows that quantum coherence plays a necessary and sufficient role in RSP. Our identifier can apply to any resource state with the minimum settings to test the performance of RSP and does not need to optimize the RSP protocol. Experimentally, we implement RSP with high-quality different source states generated from polarization-Sagnac-interferometer, showing our identifier can effectively score RSP and describe the resource state property. Our method reveals the sufficient and necessary condition of the quantum beneficial effect for realizing RSP, which helps practical situations for testing RSP in quantum networks.

Keywords: Quantum remote state preparation, Quantum coherence, Quantum state tomography