Probabilistic Distillation of Quantum Coherence


The ability to distill quantum coherence is key for the implementation of quantum technologies; however, such a task cannot always be accomplished with certainty. Here we develop a general framework of probabilistic distillation of quantum coherence, characterizing the maximal probability of success in the operational task of extracting maximally coherent states in a one-shot setting. We investigate distillation under different classes of free operations, highlighting differences in their capabilities and establishing their fundamental limitations in state transformations. We first provide a geometric interpretation for the maximal success probability, showing that under maximally incoherent operations (MIO) and dephasing-covariant incoherent operations (DIO) the problem can be further simplified in to efficiently computable semidefinite programs. Exploiting these results, we find that DIO and its subset of strictly incoherent operations (SIO) have equal power in probabilistic distillation of coherence from pure input states, while MIO are strictly stronger. We prove a fundamental no-go result: distilling coherence from any full-rank state is impossible even probabilistically. We then present a phenomenon which prohibits any trade-off between the maximal success probability and the distillation fidelity beyond a certain threshold. Finally, we consider probabilistic distillation assisted by a catalyst and demonstrate, with specific examples, its superiority to the deterministic case.

Physical Review Letters
Xin Wang
Xin Wang
Associate Professor

Prof. Xin Wang founded the QuAIR lab at HKUST(Guangzhou) in June 2023. His research primarily focuses on better understanding the limits of information processing with quantum systems and the power of quantum artificial intelligence. Prior to establishing the QuAIR lab, Prof. Wang was a Staff Researcher at the Institute for Quantum Computing at Baidu Research, where he concentrated on quantum computing research and the development of the Baidu Quantum Platform. Notably, he spearheaded the development of Paddle Quantum, a Python library designed for quantum machine learning. From 2018 to 2019, Prof. Wang held the position of Hartree Postdoctoral Fellow at the Joint Center for Quantum Information and Computer Science (QuICS) at the University of Maryland, College Park. He earned his doctorate in quantum information from the University of Technology Sydney in 2018, under the guidance of Prof. Runyao Duan and Prof. Andreas Winter. In 2014, Prof. Wang obtained his B.S. in mathematics (with Wu Yuzhang Honor) from Sichuan University.