  After the observation of non-zero $\theta_{13}$ the goal has shifted to
observe $CP$ violation in the leptonic sector. Neutrino oscillation experiments
can, directly, probe the Dirac $CP$ phases. Alternatively, one can measure $CP$
violation in the leptonic sector using Leptonic Unitarity Quadrangle(LUQ). The
existence of Standard Model (SM) gauge singlets - sterile neutrinos - will
provide additional sources of $CP$ violation. We investigate the connection
between neutrino survival probability and rephasing invariants of the
$4\times4$ neutrino mixing matrix. In general, LUQ contain eight geometrical
parameters out of which five are independent. We obtain $CP$
asymmetry($P_{\nu_f\rightarrow\nu_{f'}}-P_{\bar{\nu}_f\rightarrow\bar{\nu}_{f'}}$)
in terms of these independent parameters of the LUQ and search for the
possibilities of extracting information on these independent geometrical
parameters in short baseline(SBL) and long baseline(LBL) experiments, thus,
looking for constructing LUQ and possible measurement of $CP$ violation. We
find that it is not possible to construct LUQ using data from LBL experiments
because $CP$ asymmetry is sensitive to only three of the five independent
parameters of LUQ. However, for SBL experiments, $CP$ asymmetry is found to be
sensitive to all five independent parameters making it possible to construct
LUQ and measure $CP$ violation.
