Quantum gates and protocols with spherical wigner functions

The fundamental concepts and operations of quantum information theory are considered in the framework of a phase space formulation of quantum mechanics, where the states of one or several qubits are represented by a specific continuous quasiprobability distribution function on the Bloch sphere or on its generalizations. The function we use is the spherical Wigner function. It is shown that the usual transformations of quantum information theory are certain rotations or more general transformations of this Wigner function. We show that the standard teleportation and dense coding protocols can be appropriately formulated in terms of the Wigner function.