  We study the heat transfer between two finite quantum systems initially at
different temperatures. We find that a recently proposed fluctuation theorem
for heat exchange, namely the exchange fluctuation theorem [C. Jarzynski and D.
K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)], does not generally hold in the
presence of a finite heat transfer as in the original form proved for weak
coupling. As the coupling is weakened, the deviation from the theorem and the
heat transfer vanish in the same order of the coupling. We then discover a
condition for the exchange fluctuation theorem to hold in the presence of a
finite heat transfer, namely the commutable-coupling condition.
  We explicitly calculate the deviation from the exchange fluctuation theorem
as well as the heat transfer for simple models. We confirm for the models that
the deviation indeed has a finite value as far as the coupling between the two
systems is finite except for the special point of the commutable-coupling
condition. We also confirm analytically that the commutable-coupling condition
indeed lets the exchange fluctuation theorem hold exactly under a finite heat
transfer.
