  In the experimental determination of the population transfer efficiency
between discrete states of a coherently driven quantum system it is often
inconvenient to measure the population of the target state. Instead, after the
interaction that transfers the population from the initial state to the target
state, a second interaction is applied which brings the system back to the
initial state, the population of which is easy to measure and normalize. If the
transition probability is $p$ in the forward process, then classical intuition
suggests that the probability to return to the initial state after the backward
process should be $p^2$. However, this classical expectation is generally
misleading because it neglects interference effects. This paper presents a
rigorous theoretical analysis based on the SU(2) and SU(3) symmetries of the
propagators describing the evolution of quantum systems with two and three
states, resulting in explicit analytic formulas that link the two-step
probabilities to the single-step ones. Explicit examples are given with the
popular techniques of rapid adiabatic passage and stimulated Raman adiabatic
passage. The present results suggest that quantum-mechanical probabilities
degrade faster in repeated processes than classical probabilities. Therefore,
the actual single-pass efficiencies in various experiments, calculated from
double-pass probabilities, might have been greater than the reported values.
