  Quantum coherence and quantum entanglement are two different manifestations
of the superposition principle. In this article we show that the right choice
of basis to be used to estimate coherence is the separable basis. The quantum
coherence estimated using the Bell basis does not represent the coherence in
the system, since there is a coherence in the system due to the choice of the
basis states. We first compute the entanglement and quantum coherence in the
two qubit mixed states prepared using the Bell states and one of the states
from the computational basis. The quantum coherence is estimated using the
l1-norm of coherence, the entanglement is measured using the concurrence and
the mixedness is measured using the linear entropy. Then we estimate these
quantities in the Bell basis and establish that coherence should be measured
only in separable basis, whereas entanglement and mixedness can be measured in
any basis. We then calculate the teleportation fidelity of these mixed states
and find the regions where the states have a fidelity greater than the
classical teleportation fidelity. We also examine the violation of the
Bell-CHSH inequality to verify the quantum nonlocal correlations in the system.
The estimation of the above mentioned quantum correlations, teleportation
fidelity and the verification of Bell-CHSH inequality is also done for
bipartite states obtained from the tripartite systems by the tracing out of one
of their qubits. We find that for some of these states teleportation is
possible even when the Bell-CHSH inequality is not violated, signifying that
nonlocality is not a necessary condition for quantum teleportation.
