  A new thermodynamic inequality is derived which leads to the maximum work
that can be extracted from multi-heat baths with the assistance of discrete
quantum feedback control. The maximum work is determined by the free-energy
difference and a generalized mutual information content between the
thermodynamic system and the feedback controller. This maximum work can exceed
that in conventional thermodynamics and, in the case of a heat cycle with two
heat baths, the heat efficiency can be greater than that of the Carnot cycle.
The consistency of our results with the second law of thermodynamics is ensured
by the fact that work is needed for information processing of the feedback
controller.
