Janus-faced nature of q-deformed states and estimation of the quadrature moments from optical tomogram

Abstract

In this work, we derive the optical tomograms of various $q$-deformed quantum states. 
We found that irrespective of the deformation parameter $q$, the Janus-faced nature of the quantum states manifests in their corresponding optical tomograms. A general method to estimate the quadrature moments from the optical tomograms of any $q$-deformed states is also derived. We also note that this technique can be used in high-precision experiments to observe deviations from the standard quantum mechanical behavior.