  Quantum magnonics, an emerging field focusing on the study of magnons for
quantum applications, requires precise measurement methods capable of resolving
single magnons. Existing techniques introduce additional dissipation channels
and are not apt for magnets in free space. Brillouin light scattering (BLS) is
a well-established technique for probing the magnetization known for its high
sensitivity and temporal resolution. The coupling between magnons and photons
is controlled by a laser input, so it can be switched off when a measurement is
not needed. In this article, we theoretically investigate the efficacy of BLS
for quantum tomography of magnons. We model a finite optomagnonic waveguide,
including the optical noise added by the dielectric, to calculate the
signal-to-noise ratio (SNR). We find that the SNR is typically low due to a
small magneto-optical coupling; nevertheless, it can be significantly enhanced
by injecting squeezed vacuum into the waveguide. We reconstruct the density
matrix of the magnons from the statistics of the output photons using a maximum
likelihood estimate. The classical component of a magnon state, defined as the
regions of positive Wigner function, can be reconstructed with a high accuracy
while the non-classical component necessitates either a higher SNR or a larger
dataset. The latter requires more compact data structures and advanced
algorithms for post-processing. The SNR is limited partially by the input laser
power that can be increased by designing the optomagnonic cavity with a heat
sink.
