Some of the asymmetric three qubit W states are used for perfect teleportation, superdense coding and quantum information splitting. We present the protocols for the optimal distillation of the asymmetric as well as the symmetric W states from a single copy of any three qubit W class pure state.

n th root of a Lie algebra and its dual (that is fractional supergroup ) based on the permutation group S n invariant forms is formulated in the Hopf algebra formalism. Detailed discussion of S 3 -graded sl(2) algebras is done.

√ 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,

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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.