  We derive different relations quantifying duality in a generic two-way
interferometer. These relations set different upper bounds to the visibility V
of the fringes measured at the output port of the interferometer. A hierarchy
of inequalities is presented which exhibits the influence of the availability
to the experimenter of different sources of which-way information contributing
to the total distinguishability D of the ways. For mixed states and unbalanced
interferometers an inequality is derived, V^2+ Xi^2 \leq 1, which can be more
stringent than the one associated with the distinguishability (V^2+ D^2 \leq
1).

Quantum Physics