title: Quantum uncertainty switches on or off the error-disturbance tradeoff.
abstract: The indeterminacy of quantum mechanics was originally presented by Heisenberg through the tradeoff between the measuring error of the observable A and the consequential disturbance to the value of another observable B. This tradeoff now has become a popular interpretation of the uncertainty principle. However, the historic idea has never been exactly formulated previously and is recently called into question. A theory built upon operational and state-relevant definitions of error and disturbance is called for to rigorously reexamine the relationship. Here by putting forward such natural definitions, we demonstrate both theoretically and experimentally that there is no tradeoff if the outcome of measuring B is more uncertain than that of A. Otherwise, the tradeoff will be switched on and well characterized by the Jensen-Shannon divergence. Our results reveal the hidden effect of the uncertain nature possessed by the measured state, and conclude that the state-relevant relation between error and disturbance is not almosteverywhere a tradeoff as people usually believe.
authors.affiliation: Kuang Yaming Honors School and Department of Physics, Nanjing University, Nanjing, Jiangsu 210023, China.|Hefei National Laboratory for Physical Sciences at Microscale, The CAS Center for Excellence in QIQP and the Synergetic Innovation Center for QIQP; Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Yu-Xiang
authors.initials: YX
authors.lastname: Zhang
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale, The CAS Center for Excellence in QIQP and the Synergetic Innovation Center for QIQP; Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Zu-En
authors.initials: ZE
authors.lastname: Su
authors.affiliation: School of Physics and Optoelectronic Engineering, Xidian University, Xi'an 710071, China.
authors.forename: Xuanmin
authors.initials: X
authors.lastname: Zhu
authors.affiliation: Kuang Yaming Honors School and Department of Physics, Nanjing University, Nanjing, Jiangsu 210023, China.
authors.forename: Shengjun
authors.initials: S
authors.lastname: Wu
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale, The CAS Center for Excellence in QIQP and the Synergetic Innovation Center for QIQP; Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Zeng-Bing
authors.initials: ZB
authors.lastname: Chen