  Jarzynski equality and related fluctuation theorems can be formulated for
various setups. Such an equality was recently derived for nonunitary quantum
evolutions described by unital quantum operations, i.e., for completely
positive, trace-preserving maps, which preserve the maximally mixed state. We
analyze here a more general case of arbitrary quantum operations on finite
systems and derive the corresponding form of the Jarzynski equality. It
contains a correction term due to nonunitality of the quantum map. Bounds for
the relative size of this correction term are established and they are applied
for exemplary systems subjected to quantum channels acting on a
finite-dimensional Hilbert space.
