  Quantum discord plays a pragmatic role in analyzing nonclassical feature of
quantum correlations beyond entanglement. It is used in several information
processing protocols which lacks sufficient amount of entanglement to be used
as a resource. We have provided with an analytical method of detecting quantum
discord of an arbitrary two qubit state. We have formulated a set of necessary
and sufficient conditions for any two qubit state to be a both-way non-zero
quantum discord state. As quantum discord is asymmetric in nature, we have
framed the set of if and only if conditions for a two qubit state to be
classical-quantum as well for it to be quantum-classical. Interestingly, not
only correlation tensor but also local Bloch vector(corresponding to the
classical party) plays a role for detecting the state to be a positive discord
state.
