Higher order quantum vortex

Abstract: In this article we present a quantum theoretical framework of photons entangled in higher order modes like Ince-Gauss modes. Ince-Gauss modes are the natural solution of the quantum harmonic oscillator in elliptical coordinates. These modes are defined by an additional quantum number, the ellipticity parameter which is expected to play a major role in continuous variable quantum key distribution protocols. Although such quantum states have been realized in experiments but a proper theoretical framework has been missing. We aim to address this shortcoming with our article.