  Three different measurements have been reported for the ground state
quadrupole polarizability in the singly ionized barium (Ba$^+$) which disagree
with each other. Our calculation of this quantity using the relativistic
coupled-cluster method disagrees with two of the experimental values and is
within the error bars of the other. We discuss the issues related to the
accuracy of our calculations and emphasize the need for further experiments to
measure the quadrupole polarizability for this state and/or the 5D states.
