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The state of an atom in a bipartite qubit, Jaynes-Cummings (JC) oranti-Jaynes-Cummings (aJC) interaction is described by a reduced densityoperator. The purity of the state has been measured by taking the trace of thesquare of the reduced density operator. In this article, we define the squareof the reduced density operator as the state purity operator, composed of acompletely pure state part and a completely mixed state part. The coefficientof the completely mixed state part is the mixed state measure, formallyobtained as the determinant of the reduced density operator and it is thereforedirectly related to tangle, the square of concurrence of the bipartite system.Expressed in various equivalent forms, the mixed state measure provides all thecharacteristic elements of state purity or entanglement, such as eigenvalues ofthe reduced density operator, nonclassicality measures and a state puritycomplex amplitude. The argument of the state purity complex amplitude in polarform is the phase of the state purity measure, which defines the degree ofpurity of the state. We find that the degree of purity and concurrence arecomplementary quantifiers satisfying a complementarity relation.

On atomic state purity operator, degree of state purity and concurrence in the JC and anti-JC models