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

从量子态的“叠加”中出现的量子相干被广泛用于各种信息处理任务中。近年来，多级量子相干的资源理论引起了人们的广泛关注。在本文中，我们主要在多层次一致性的理论框架中研究通过自由操作进行的资源纯状态转换。我们证明，通过完全正且跟踪的不增加k-相干保持映射，可以以非零概率互转换任何两个多级相干资源纯状态。同时，我们给出了k下两个多级相干资源纯态互转换的条件-保持一致性的操作。此外，我们得到在多级一致性的资源理论框架，没有资源状态是分离的，即，给定的多级相干纯状态| ψ >，存在另一个多级相干纯态| φ >和ķ -coherence -preserving操作Λ _ķ，使得Λ _ķ（|φ>）= | ψ >。