  We examine the fluctuation theorems which traditionally have been studied for
classical systems and enquire if they can be extended to the quantum domain,
especially at low temperatures. The example chosen is that of a problem which
has proven to be of great interest in the context of Landau diamagnetism viz.
the quantized motion of an electron in a magnetic field and in a dissipative
environment. It is established from first principles that the quantum work
operator W has a Gaussian distribution even though the system under
consideration has a four dimensional phase space. The parameter $\alpha$ in the
fluctuation theorem $p(W )/p(-W) = exp(\alpha W)$ depends on the system
dynamics and has characteristic quantum features, especially at low
temperatures. Certain unique low temperature signatures are also discussed.
