Quantum measurements of magnons are crucial for the development of quantum applications based on magnonics. We theoretically analyze the efficacy of Brillouin light scattering (BLS) for quantum tomography of magnons. We consider a finite-length optomagnonic waveguide made of Yttrium Iron Garnet (YIG), and derive the relation between the transmitted photons and the state of the magnons. While the signal-to-noise ratio (SNR) is low due to a small magneto-optical coupling, we show that significant improvement can be achieved by injecting squeezed vacuum of photons. Then, we discuss a protocol of reconstructing the magnon’s density matrix based on the observed statistics of the transmitted photons, using maximum likelihood principle. We find that the classical component of a magnon state, defined as the regions of positive Wigner function, can be reconstructed with a high accuracy. Reconstructing the nonclassical component requires improved SNR or larger datasets, and we explore potential methods to achieve these goals.
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