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Coherence distillation is one of the central problems in the resource theory of coherence. In this Letter, we complete the deterministic distillation of quantum coherence for a finite number of coherent states under strictly incoherent operations. Specifically, we find the necessary and sufficient condition for the transformation from a mixed coherent state into a pure state via strictly incoherent operations, which recovers a connection between the resource theory of coherence and the algebraic theory of majorization lattice. With the help of this condition, we present the deterministic coherence distillation scheme and derive the maximum number of maximally coherent states obtained via this scheme.
We introduce and study the task of assisted coherence distillation. This task arises naturally in bipartite systems where both parties work together to generate the maximal possible coherence on one of the subsystems. Only incoherent operations are a
Coherence distillation is a central topic of the resource theory of coherence and various coherence distillation protocols were proposed. In this paper, we investigate the optimal probabilistic coherence distillation protocol, whose aim is to transfo
We characterize the operational task of environment-assisted distillation of quantum coherence under different sets of free operations when only a finite supply of copies of a given state is available. We first evaluate the one-shot assisted distilla
The remarkable phenomenon of catalyst tells us that adding a catalyst could help state transformation. In this paper, we consider the problem of catalyst-assisted probabilistic coherence distillation for mixed states under strictly incoherent operati
Quantum coherence, which quantifies the superposition properties of a quantum state, plays an indispensable role in quantum resource theory. A recent theoretical work [Phys. Rev. Lett. textbf{116}, 070402 (2016)] studied the manipulation of quantum c