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Conditions for coherence transformations under incoherent operations
Shuanping Du, Zhaofang Bai, Yu Guo
TL;DR
The paper addresses whether coherence transformations can be characterized analogously to Nielsen's theorem. It uses majorization to characterize pure-state transformations under incoherent operations, deriving incomparable coherence types and coherent catalysts, while leaving mixed-state transformations and infinite-dimensional settings open.
Problem
The paper asks whether coherence manipulation admits a counterpart to Nielsen's theorem, including whether one of two states can always be transformed into the other under incoherent operations.
Method
The paper characterizes pure-state transformations under incoherent operations through majorization and provides a constructive method for finding the transforming operation.
Results
Pure-state transformations are completely characterized by majorization, and the results identify incomparable coherence types and coherent catalysts for certain otherwise forbidden transformations.
Takeaways & Limitations
The results identify the structure governing pure-state interconvertibility and provide consequences for coherent catalysts and the construction of coherence measures.
Takeaways & Limitations
The analysis primarily characterizes pure states, while sufficient conditions for catalysts, mixed-state transformations, and infinite-dimensional systems remain open or outside the developed setting.
Abstract
from arXiv · showhide
We build the counterpart of the celebrated Nielsen's theorem for coherence manipulation in this paper. This offers an affirmative answer to the open question: whether, given two states $ρ$ and $σ$, either $ρ$ can be transformed into $σ$ or vice versa under incoherent operations [Phys. Rev. Lett. \textbf{113}, 140401(2014)]. As a consequence, we find that there exist essentially different types of coherence. Moreover, incoherent operations can be enhanced in the presence of certain coherent states. These extra states are coherent catalysts: they allow uncertain incoherent operations to be realized, without being consumed in any way. Our main result also sheds a new light on the construction of coherence measures.
Appendix : Transition of mixed states
The appendix constructs an incoherent operation that maps any quantum state ρ to an incoherent mixed state σ by removing off-diagonal elements and then applying a second operation.
- The constructed operation removes ρ's off-diagonal elements while preserving its diagonal elements.This produces a state containing the coefficients λ_i=<i|ρ|i⟩ on the incoherent basis.
- A second incoherent operation is applied after the first operation to obtain the target incoherent state σ.
- The composition Φ=Φ2◦Φ1 is an incoherent operation satisfying Φ(ρ)=σ.