  Based on trajectory dependent path probability formalism in state space, we
derive generalized entropy production fluctuation relations for a quantum
system in the presence of measurement and feedback. We have obtained these
results for three different cases: (i) the system is evolving in isolation from
its surroundings; (ii) the system being weakly coupled to a heat bath; and
(iii) system in contact with reservoir using quantum Crooks fluctuation
theorem. In case (iii), we build on the treatment carried out in [H. T. Quan
and H. Dong, arxiv/cond-mat: 0812.4955], where a quantum trajectory has been
defined as a sequence of alternating work and heat steps. The obtained entropy
production fluctuation theorems retain the same form as in the classical case.
The inequality of second law of thermodynamics gets modified in the presence of
information. These fluctuation theorems are robust against intermediate
measurements of any observable performed with respect to von Neumann projective
measurements as well as weak or positive operator valued measurements.
