Purification of mixed states in Quantum Mechanics, by which we mean the transformation into pure states, has been viewed as an {it Operation} in the sense of Kraus et al and explicit {it Kraus Operators} cite{kra1,kra2,kra3} have been constructed for two seperate purification protocols. The first one, initially due to Schrodinger cite{sch} and subsequently elaborated by Sudarshan et al cite{sudar}, is based on the {it preservation of probabilities}. We have constructed a second protocol here based on {it optimization of fidelities}. Both purification protocols have been implemented on a single qubit in an attempt to improve the fidelity of the purified post measurement state of the qubit with the initial pure state. We have considered both {it complete} and {it partial} measurements and have established bounds and inequalities for various fidelities. We show that our purification protocol leads to better state reconstruction, most explicitly so, when partial measurements are made.
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