Experimental investigation of measurement incompatibility of mutually unbiased bases
Yu Guo,
Shuming Cheng,
Xiao-Min Hu,
Bi-Heng Liu,
Yun-Feng Huang,
Chuan-Feng Li,
Guang-Can Guo
Affiliations
Yu Guo
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
Shuming Cheng
Corresponding authors.; The Department of Control Science and Engineering, Tongji University, Shanghai 201804, China; Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai 201804, China; Institute for Advanced Study, Tongji University, Shanghai 200092, China
Xiao-Min Hu
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
Bi-Heng Liu
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China; Corresponding authors.
Yun-Feng Huang
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
Chuan-Feng Li
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
Guang-Can Guo
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
Incompatible measurements are of fundamental importance to revealing the peculiar features of quantum theory, and are also useful resources in various quantum information tasks. In this work, we investigate the quantum incompatibility of mutually unbiased bases (MUBs) within the operational framework of quantum resource theory, and report an experimental validation via the task of state discrimination. In particular, we construct an experimentally friendly witness to detect incompatible MUBs, based on the probability of correctly discriminating quantum states. Furthermore, we prove that the noise robustness of MUBs can be retrieved from violating the above witness. Finally, we experimentally test the incompatibility of MUBs of dimensionality ranging from 2 to 4, and demonstrate that it is more robust to noise, as either the dimensionality of measurements or the number of MUBs increases. Our results may aid the exploration of the essential roles of incompatible measurements in both theoretical and practical applications in quantum information.
