Generalized physically incoherent operations

Quantum coherence is an intrinsic property within a single quantum system. Many different coherent resource theories have been proposed to characterize this property within the framework of resource theory. This difference is based on the difference in the identification of ``free'' operations. In this article, generalized physically incoherent operations, which are strictly contained in the intersection of incoherent operations and dephasing-covariant operations (dephasing-covariant incoherent incoherent operations), are introduced. We characterize the Kraus operators of dephasing-covariant incoherent incoherent operations and generalized physically incoherent operations, and further study the coherent state transformations under generalized physically incoherent operations. Specifically, we investigate the constraints imposed by the rank of the initial state on the extraction of a pure coherent state. Additionally, we present a sufficient condition for the transformation from a mixed state to a pure state ensemble.