Experimental demonstration of tight duality relation inthree-path interferometer

doi:10.1088/1674-1056/ab7ea2

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, C² + D² ≤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 l₁-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.

Keywords: duality relation multi-path interferometer principle of complementarity foundations of quantum mechanics

Received: 22 February 2020
Revised: 04 March 2020
Accepted manuscript online:

PACS:	03.65.-w	(Quantum mechanics)
	42.50.Xa	(Optical tests of quantum theory)
	03.65.Ta	(Foundations of quantum mechanics; measurement theory)
	42.50.Ex	(Optical implementations of quantum information processing and transfer)

Fund: Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0302700 and 2017YFA0304100), the National Natural Science Foundation of China (Grant Nos. 11822408, 11674304, 11774335, 61490711, 11474267, 11821404, 11325419, 11904356, and 91321313), the Youth Innovation Promotion Association, Chinese Academy of Sciences (Grant No. 2017492), the Foundation for Scientific Instrument and Equipment Development, Chinese Academy of Sciences (Grant No. YJKYYQ20170032), the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDY-SSW-SLH003), the Fundamental Research Funds for the Central Universities, China (Grant Nos. WK2470000026 and WK2030000008), Science Foundation of Chinese Academy of Sciences (Grant No. ZDRW-XH-2019-1), Anhui Initiative in Quantum Information Technologies, China (Grant Nos. AHY020100, AHYPT003, and AHY060300), the National Postdoctoral Program for Innovative Talents of China (Grant No. BX20180293), and the China Postdoctoral Science Foundation (Grant No. 2018M640587).

Corresponding Authors: Jian-Shun Tang, Chuan-Feng Li
E-mail: tjs@ustc.edu.cn;cfli@ustc.edu.cn

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Zhi-Jin Ke(柯芝锦), Yu Meng(孟雨), Yi-Tao Wang(王轶韬), Shang Yu(俞上), Wei Liu(刘伟), Zhi-Peng Li(李志鹏), Hang Wang(汪航), Qiang Li(李强), Jin-Shi Xu(许金时), Jian-Shun Tang(唐建顺), Chuan-Feng Li(李传锋), Guang-Can Guo(郭光灿) Experimental demonstration of tight duality relation inthree-path interferometer 2020 Chin. Phys. B 29 050307

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