√ d }, where all other ddimensional coherent states can be generated from it by means of incoherent operations [12].We focus on particular quantum operations for which measurement outcomes are retained as stated in [12]. These quantum operations are defined by Kraus operators {K i } such that ∑ i K † i K i = I and, for all i and ρ ∈ I,

We present an optimal probabilistic protocol to distill quantum coherence. Inspired by a specific entanglement distillation protocol, our main result yields a strictly incoherent operation that produces one of a family of maximally coherent states of variable dimension from any pure quantum state. We also expand this protocol to the case where it is possible, for some initial states, to avert any waste of resources as far as the output states are concerned, by exploiting an additional transformation into a suitable intermediate state. These results provide practical schemes for efficient quantum resource manipulation.

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