Optical Maxwell's demon phase space theory and its efficiency improvement to 90 % with local online squeezing

A Maxwell's demon is a being with the ability to extract work from information. Recently, an optical simulator of Maxwell's demon was experimentally demonstrated. Here, we formulate the power of Maxwell's demon using the phase space method, which enables a clear explanation of power optimality at 16/27. We apply our phase space method to determine if local online squeezing might improve the demon's performance. Local online squeezing will alter photon statistics, and it is difficult to derive a strict (no approximation) closed formula for efficiency in the photon number space. We observe that phase space shows improvement in the demon's efficiency from 59 percent to 90 percent with online squeezing, for approximately 51.93 percent enhancement. Our work provides a simple and deterministic method to enhance the efficiency of Maxwell's demon.