  The issue of interference and which-way information is addressed in the
context of 3-slit interference experiments. A new path distinguishability
${\mathcal D_Q}$ is introduced, based on Unambiguous Quantum State
Discrimination (UQSD). An inequality connecting the interference visibility and
path distinguishability, ${\mathcal V} + {2{\mathcal D_Q}\over 3- {\mathcal
D_Q}} \le 1$, is derived which puts a bound on how much fringe visibility and
which-way information can be simultaneously obtained. It is argued that this
bound is tight. For 2-slit interference, we derive a new duality relation which
reduces to Englert's duality relation and Greenberger-Yasin's duality relation,
in different limits.
