  For classical Markovian stochastic systems, past and future events become
statistically independent when conditioned to a given state at the present
time. Memory non-Markovian effects break this condition, inducing a
non-vanishing conditional past-future correlation. Here, this classical memory
indicator is extended to a quantum regime, which provides an operational
definition of quantum non-Markovianity based on a minimal set of three
time-ordered quantum system measurements and post-selection. The detection of
memory effects through the measurement scheme is univocally related to
departures from Born-Markov and white noise approximations in quantum and
classical environments respectively.
