  Wave-particle duality relations are fundamental for quantum physics. Previous
experimental studies of duality relations mainly focus on the quadratic
relation $D^2+V^2\leq1$, based on symmetric beam interference, while a linear
form of the duality relation, predicated earlier theoretically, has never been
experimentally tested. In addition, the difference between the quadratic form
and the linear form has not been explored yet. In this work, with a designed
asymmetric beam interference and by utilizing the polarization degree of
freedom of the photon as a which-way detector, we experimentally confirm both
forms of the duality relations. The results show that more path information is
obtained in the quadratic case. Our findings reveal the difference between the
two duality relations and have fundamental implications in better understanding
these important duality relations.
