Experimental demonstration of tight duality relation in three-path interferometer

Ke Zhi-Jin^{1, 2}, Meng Yu^{1, 2}, Wang Yi-Tao^{1, 2}, Yu Shang^{1, 2}, Liu Wei^{1, 2}, Li Zhi-Peng^{1, 2}, Wang Hang^{1, 2}, Li Qiang^{1, 2}, Xu Jin-Shi^{1, 2}, Tang Jian-Shun^{1, 2, †}, Li Chuan-Feng^{1, 2, ‡}, Guang-Can Guo^{1, 2}

Theoretical diagram of the tight new duality relation in multipath interferometers. C and D are the horizontal and vertical coordinates, respectively. The black line is a quarter of a unit cycle, which is described by Eq. (1) and used as a reference. The red line is a part of an ellipse, whose center O and semiminor axis OB lie on the line C = D, and semimajor axis OA is parallel to the line C+D = 1. This ellipse is described by Eq. (2) when n = 6. The union of yellow and pink regions reveals the area that the tight duality relation bounds in a six-path interferometer.