  We propose a new thermodynamic equality and several inequalities concerning
the relationship between work and information for an isothermal process with
Maxwell's demon. Our approach is based on the formulation a la Jarzynski of the
thermodynamic engine and on the quantum information-theoretic characterization
of the demon. The lower bound of each inequality, which is expressed in terms
of the information gain by the demon and the accuracy of the demon's
measurement, gives the minimum work that can be performed on a single heat bath
in an isothermal process. These results are independent of the state of the
demon, be it in thermodynamic equilibrium or not.
