  In the derivation of local bound of a Bell's inequality, the response
functions corresponding to the different outcomes of measurements are fixed by
the relevant hidden variables irrespective of the fact if the measurement is
unsharp. In the context of a recent result by Spekkens that tells even in an
ontological model the unsharp observable cannot be assigned a deterministic
response function, we derive a modified local bound of CHSH inequality in
unsharp measurement scenario. We consider response function for a given POVM
which is determined by the response functions of the relevant projectors
appearing in its spectral representation. In this scenario, the local bound of
CHSH inequality is found to be dependent on the unsharpness parameter. This
then enables us to show that the quantum violation of CHSH inequality for
unbiased spin-POVMs occurs whenever there is violation for their sharp
counterpart. For the case of biased POVMs, it is shown that the quantum
violation of CHSH inequality can be obtained for ranges of sharpness parameter
for which no violation obtained using standard local bound of CHSH inequality.

Quantum Physics