Quadrature uncertainty and information entropy of quantum elliptical vortex states

We study the quadrature uncertainty of the quantum elliptical vortex state using the associated Wigner function. Deviations from the minimum uncertainty states were observed due to the absence of Gaussianity. We further observed that there exists an optimum value of ellipticity which gives rise to the maximum entanglement of the two modes of the quantum elliptical vortex states. In our study of entropy, we noticed that with increasing vorticity, entropy increases for both the modes. A further increase in ellipticity reduces the entropy thereby resulting in a loss of information carrying capacity. We check the validity of the entropic inequality relations, namely the subaddivity and the Araki–Lieb inequality. The latter was satisfied only for a very small range of the ellipticity of the vortex, while the former seemed to be valid at all values.