Experiment data. The orange solid line is the theoretical tight bound of duality relation in a three-path interferometer, described by Eq. (3). The circle points are the experimental results of the state with maximal coherence. They lie on the theoretical bound and they move along the bound when θ in the indicator states {|ηi〉} varies. While the triangle and rhombus points are the experimental results of two other states without maximal coherence. The states represented by triangle have much coherence than those represented by rhombus. We use l1-norm coherence measure to quantify all these states. The black dash line is the quadrant described by Eq. (1), and it is used as a reference.