Transformations of multilevel coherent states under coherence-preserving operations

Quantum coherence, emerging from the “superposition” of quantum states, is widely used in various information processing tasks. Recently, resource theory multilevel coherence attracting substantial attention. In this paper, we mainly study transformations pure states via free operations theoretical framework for coherence. We prove that any two coherent can be interconverted with a nonzero probability completely positive and trace non-increasing k-coherence-preserving map. Meanwhile, present condition interconversions under operations. addition, obtain resource-theoretic no state isolated, is, given ∣ψ〉, there exists another ∣ϕ〉 operation Λk, such Λk(∣ϕ〉) = ∣ψ〉.