  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.
