  We report a scheme for generation of high-order vortex states using two-mode
photon-number squeezed states, generated via the non-linear process of
Spontaneous Parametric Down Conversion. By applying a parametric rotation in
quadrature space $(X,Y)$, using a $\phi$ converter, the Gaussian quadrature
profile of the photon-number squeezed input state can be mapped into a
superposition of Laguerre-Gauss modes with $N$ vortices or singularities, for
an input state containing $N$ photons, thus mapping photon-number fluctuations
to interference effects in quadrature space. Our scheme has the potential to
improve measurement sensitivity beyond the Standard Quantum Limit (SQL $\propto
\sqrt{N}$), by exploiting the advantages of optical vortices, such as ease of
creation and detection, high dimensionality or topological properties, for
applications requiring reduced uncertainty, such as quantum cryptography,
quantum metrology and sensing.
