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The classification of the multipartite entanglement is an important problemin quantum information theory. We propose a class of two qubit mixed states$\sigma_{AB}=p|\chi_{1}\rangle\langle\chi_{1}|\otimes\rho_{1}+(1-p)|\chi_{2}\rangle\langle\chi_{2}|\otimes\rho_{2}$,where $|\chi_{1}\rangle=\alpha|0\rangle+\beta|1\rangle$,$|\chi_{2}\rangle=\beta|0\rangle+(-1)^{n}\alpha|1\rangle$. We have shown thatthe state $\sigma_{AB}$ represent a classical state when $n$ is odd while itrepresent a non-classical state when $n$ is even. The purification of the state$\sigma_{AB}$ is studied and found that the purification is possible if thespectral decomposition of the density matrices $\rho_{1}$ and $\rho_{2}$represent pure states. We have established a relationship between three tangle,which measures the amount of entanglement in three qubit system and thequantity $\langle\chi_{1}|\chi_{2}\rangle$, which identifies whether the twoqubit mixed state is classical or non-classical. The three qubit purified stateis then classified as a separable or biseparable or W-type or GHZ-type stateusing the quantum correlation, measured by geometric discord, of its reducedtwo qubit density matrix.

A New Method of Classification of Pure Tripartite Quantum States