  We analyze the trade-off between the amounts of information obtainable on
complementary properties of a qubit state by simultaneous measurements. We
consider a "state discrimination" scenario wherein the same measurements are
repeated, but the input states must be guessed in every run. We find a general
complementarity relation for path-phase guesses by any generalized measurements
in this scenario. The counterpart of this input-output mutual information (MI)
reveals a hitherto unknown aspect of complementarity.
