  We demonstrate the possibility of surpassing the quantum noise limit for
simultaneous multi-axis spatial displacement measurements that have zero mean
values. The requisite resources for these measurements are squeezed light beams
with exotic transverse mode profiles. We show that, in principle, lossless
combination of these modes can be achieved using the non-degenerate Gouy phase
shift of optical resonators. When the combined squeezed beams are measured with
quadrant detectors, we experimentally demonstrate a simultaneous reduction in
the transverse x- and y- displacement fluctuations of 2.2 dB and 3.1 dB below
the quantum noise limit.
