  Information spreads in time. For example, correlations dissipate when the
correlated system locally couples to a third party, such as the environment.
This simple but important fact forms the known quantum data-processing
inequality. Here we theoretically uncover the quantum fluctuation theorem
behind the quantum informational inequality. The fluctuation theorem
quantitatively predicts the statistics of the underlying stochastic quantum
process. To fully capture the quantum nature, the fluctuation theorem
established here is extended to the quasiprobability regime. We also
experimentally apply an interference-based method to measure the amplitudes
composing the quasiprobability and verify our established fluctuation theorem
by the IBM quantum computer.
