  The two-time measurement scheme is well studied in the context of quantum
fluctuation theorem. However, it becomes infeasible when the random variable
determined by a single measurement trajectory is associated with the
von-Neumann entropy of the quantum states. We employ the one-time measurement
scheme to derive a Jarzynski-like equality of nonequilibrium information
production by proposing an information production distribution based on the
quantum cross entropy. The derived equality further enables one to explore the
roles of the quantum cross entropy in quantum communications, quantum machine
learning and quantum thermodynamics.
