  We derive integral quantum fluctuation theorems and quantum Jarzynski
equalities for a feedback-controlled system and a memory which registers
outcomes of the measurement. The obtained equalities involve the information
content, which reflects the information exchange between the system and the
memory, and take into account the back action of a general measurement contrary
to the classical case. The generalized second law of thermodynamics under
measurement and feedback control are reproduced from these equalities.
