  It is known that the witness operator is useful in the detection and
quantification of entangled states. This motivated us for the construction of
the family of witness operators that can detect many mixed entangled states.
This family of witness operators is then used to estimate the lower bound of
concurrence of the detected mixed entangled states. Our method of construction
of witness operator is important in the sense that it will estimate a better
lower bound of concurrence of the entangled states in arbitrary $d_{1}\otimes
d_{2} (d_{1}\leq d_{2})$ dimensional system compared to the lower bound of the
concurrence given in \cite{kchen}. We have shown the significance of our
constructed witness operator by detecting many bound entangled states that are
not detected by the earlier methods and then we use the expectation value of
the witness operator to estimate the lower bound of the concurrence of those
bound entangled states.
