  We address the experimental estimation of Gaussian quantum discord for
two-mode squeezed thermal state, and demonstrate a measurement scheme based on
a pair of homodyne detectors assisted by Bayesian analysis which provides
nearly optimal estimation for small value of discord. Besides, though homodyne
detection is not optimal for Gaussian discord, the noise ratio to the ultimate
quantum limit, as dictacted by the quantum Cramer-Rao bound, is limited to
about 10 dB.
