Experimental test of the tradeoff relation in weak measurement

Geng Chen, Yang Zou, Xiao-Ye Xu, Jian-Shun Tang, Yu-Long Li, Yong-Jian Han, Chuan-Feng Li, Guang-Can Guo Hai-qiao Ni, Ying Yu, Mi-feng Li, Guo-wei Zha, Zhi-Chuan Niu

Published 2013-06-05Version 1

An upper bound between the information gain and state reversibility of weak measurement was first developed by Y. K. Cheong and S. W. Lee [Phys. Rev. Lett. 109, 150402 (2012)]. Their results are valid for arbitrary d-level quantum systems. In light of the commonly used qubit system in quantum information, a sharp tradeoff relation can be obtained. In this letter, this tradeoff relation is experimentally verified with polarization encoded single photons from a quantum dot. Furthermore, a complete traversal of weak measurement operators is realized, and the mapping to the least upper bound of this tradeoff relation is obtained. Our results complement the theoretical work and provide a universal ruler for the characterization of weak measurements.