Janus-faced tomograms and retrieval of quadrature moments for $q$-deformed states

In this work, we derive the optical tomograms of various $q$-deformed quantum states. We found that the optical tomograms of the states under consideration exhibit a fascinating `Janus faced’ nature, irrespective of the deformation parameter $q$. We also derived a general method to extract the quadrature moments from the optical tomograms of any $q$-deformed states. We also note that this technique can be used in high-precision experiments to observe deviations from the standard quantum mechanical behavior.