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An explanation and an illustration of the meaning of a discrete phase-space is given. The class of a discrete Wigner transform (DWT) for the specific case of a one-qubit state is introduced. We derive the one-qubit state formalism around its formulation in terms of the DWT in detail. A novel structure of a one-qubit purity in terms of the DWT is introduced. We find a criterion for stating when a one-qubit state is either mixed or pure.
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