Coherence filtration under strictly incoherent operations

Abstract

We study the task of coherence filtration under strictly incoherent operations in this paper. The aim of this task is to transform a given state $\rho$ into another one ${\rho }^{\prime }$ whose fidelity with the maximally coherent state is maximal by using stochastic strictly incoherent operations. We find that the maximal fidelity between ${\rho }^{\prime }$ and the maximally coherent state is given by a multiple of the $\Delta$ robustness of coherence $R(ρ\|Δρ):=\min\{\uplambda|ρ\leq\uplambdaΔρ\}$, which provides $R(\rho \Vert \Delta \rho )$ an operational interpretation. Finally, we provide a coherence measure based on the task of coherence filtration.

arXiv comment6 pages. arXiv admin note: text overlap with arXiv:2206.04208

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