Experimental Demonstration of Inequivalent Mutually Unbiased Bases

Wen-Zhe Yan; Yunting Li; Zhibo Hou; Huangjun Zhu; Guo-Yong Xiang; Chuan-Feng Li; Guang-Can Guo

doi:10.1103/PhysRevLett.132.080202

Experimental Demonstration of Inequivalent Mutually Unbiased Bases

Phys Rev Lett. 2024 Feb 23;132(8):080202. doi: 10.1103/PhysRevLett.132.080202.

Authors

Wen-Zhe Yan^{1

2}, Yunting Li^{3

4

5}, Zhibo Hou^{1

2

6}, Huangjun Zhu^{3

4

5}, Guo-Yong Xiang^{1

2

6}, Chuan-Feng Li^{1

2

6}, Guang-Can Guo^{1

2

6}

Affiliations

¹ CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.
² CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
³ State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China.
⁴ Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai 200433, China.
⁵ Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China.
⁶ Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, People's Republic of China.

PMID: 38457709
DOI: 10.1103/PhysRevLett.132.080202

Abstract

Quantum measurements based on mutually unbiased bases (MUBs) play crucial roles in foundational studies and quantum information processing. It is known that there exist inequivalent MUBs, but little is known about their operational distinctions, not to say experimental demonstration. In this Letter, by virtue of a simple estimation problem, we experimentally demonstrate the operational distinctions between inequivalent triples of MUBs in dimension 4 based on high-precision photonic systems. The experimental estimation fidelities coincide well with the theoretical predictions with only 0.16% average deviation, which is 25 times less than the difference (4.1%) between the maximum estimation fidelity and the minimum estimation fidelity. Our experiments clearly demonstrate that inequivalent MUBs have different information extraction capabilities and different merits for quantum information processing.