Experimental demonstration of tight duality relation in three-path interferometer*

Abstract

Bohr’s principle of complementarity has a long history and it is an important topic in quantum theory, among which the famous example is the duality relation. The relation between visibility C and distinguishability D, C 2 + D 2 ≤ 1 , has long been recognized as the only representative of the duality relation. However, recent researches have shown that this inequality is not good enough because it is not tight for multipath interferometers. Meanwhile, a tight bound for the multipath interferometer has been put forward. Here we design and experimentally implement a three-path interferometer coupling with path indicator states. The wave property of photons is characterized by l 1-norm coherence measure, and the particle property is based on distinguishability of the indicator states. The new duality relation of the three-path interferometer is demonstrated in our experiment, which bounds the union of a right triangle and a part of elliptical area inside the quadrant of a unit circle. Data analysis confirms that the new bound is tight for photons in three-path interferometers.