Abstract
The manipulation of quantum coherence is one of the principal issues in the resource theory of coherence, with two critical topics being the purification and enhancement of coherence. Here, we present two no-go theorems for the deterministic purification of coherence and the probabilistic enhancement of coherence, respectively. Specifically, we prove that a quantum state cannot be deterministically purified if it can be expressed as a convex combination of an incoherent state and a coherent state. Besides, we give an easy-to-verified sufficient and necessary condition to determine whether a state can be probabilistically enhanced via a stochastic strictly incoherent operation. Our findings provide two feasibility criteria for the deterministic purification and the probabilistic enhancement of coherence, respectively. These results have repercussions on the understanding of quantum coherence in real quantum systems.
| Original language | English |
|---|---|
| Article number | 105301 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 55 |
| Issue number | 10 |
| DOIs | |
| State | Published - 11 Mar 2022 |
Bibliographical note
Publisher Copyright:© 2022 IOP Publishing Ltd.
Funding
We thank C L Liu for thoroughly reading the manuscript, and for many suggestions, corrections, and comments, which have certainly helped to improve this manuscript. We are grateful to two anonymous referees for providing very useful comments on earlier versions of this manuscript. This work was supported by NSF China through Grant No. 11575101.
| Funders | Funder number |
|---|---|
| National Science Foundation | 11575101 |
Keywords
- coherence manipulation
- no-go theorem
- quantum coherence