  We have experimentally realized an information engine consisting of an
optically trapped, heavy bead in water. The device raises the trap center after
a favorable "up" thermal fluctuation, thereby increasing the bead's average
gravitational potential energy. In the presence of measurement noise, poor
feedback decisions degrade its performance; below a critical signal-to-noise
ratio, the engine shows a phase transition and cannot store any gravitational
energy. However, using Bayesian estimates of the bead's position to make
feedback decisions can extract gravitational energy at all measurement noise
strengths and has maximum performance benefit at the critical signal-to-noise
ratio.
