Probabilistic distillation of quantum coherence

Fang, Kun; Wang, Xin; Lami, Ludovico; Regula, Bartosz; Adesso, Gerardo

Abstract

The ability to distill quantum coherence is pivotal for optimizing the performance 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 in a one-shot setting, establishing fundamental limitations for different classes of free operations. 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 simplified into efficiently computable semidefinite programs. Exploiting these results, we find that DIO and its subset of strictly incoherent operations have equal power in the probabilistic distillation of coherence from pure input states, while MIO are strictly stronger. We then prove a fundamental no-go result: Distilling coherence from any full-rank state is impossible even probabilistically. We further find that in some conditions the maximal success probability can vanish suddenly beyond a certain threshold in the distillation fidelity. Finally, we consider probabilistic coherence distillation assisted by a catalyst and demonstrate, with specific examples, its superiority to the unassisted and deterministic cases.

Citation

Fang, K., Wang, X., Lami, L., Regula, B., & Adesso, G. (2018). Probabilistic distillation of quantum coherence. Physical Review Letters, 121(7), doi:10.1103/physrevlett.121.070404. ISSN 0031-9007

• Journal Article Type: Article
• Acceptance Date: Aug 1, 2018
• Online Publication Date: Aug 17, 2018
• Publication Date: Aug 17, 2018
• Deposit Date: Sep 6, 2018
• Publicly Available Date: Sep 6, 2018
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 121
• Issue: 7
• Article Number: 070404
• DOI: https://doi.org/10.1103/physrevlett.121.070404
• Keywords: General Physics and Astronomy