  Entanglement lies at the heart of quantum mechanics and has no classical
analogue. It is central to the speed up achieved by quantum algorithms over
their classical counterparts. The Grover's search algorithm is one such
algorithm which enables us to achieve a quadratic speed up over any known
classical algorithm that searches for an element in an unstructured database.
Here, we analyse and quantify the effects of entanglement in the generalized
version of this algorithm for two qubits. By 'generalized', it is meant that
the use of any arbitrary single qubit unitary gate is permitted to create
superposed states. Our analysis has been firstly on a noise free environment
and secondly in the presence of noise. In the absence of noise, we establish a
relation between the concurrence and the amplitude of the final state thereby
showing the explicit effects of entanglement on the same. Moreover, the effects
of noisy channels, namely amplitude and phase damping channels are studied. We
investigate the amount of quantum correlation in the states obtained after the
phase inversion stage of the algorithm followed by interaction of those states
with the noisy environment. The quantum correlations are quantified by
geometric discord. It has been revealed that the states generated after the
effect of amplitude damping on the phase inverted states of the quantum search
algorithm possess non-zero quantum correlation even when entanglement is
absent. However, this is absent in the phase damping scenario.
