Communications in Theoretical Physics ›› 2022, Vol. 74 ›› Issue (1): 015101. doi: 10.1088/1572-9494/ac3646

• Quantum Physics and Quantum Information • Previous Articles     Next Articles

Uncertainty relation of successive measurements based on Wigner–Yanase skew information

Jun Zhang1,2,(),Jia-Ning Wei2,Zhou-Bo Duan2,Kan He2,Chang-Shui Yu3,()   

  1. 1College of Data Science, Taiyuan University of Technology, Taiyuan 030024, China
    2College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
    3School of Physics, Dalian University of Technology, Dalian 116024, China
  • Received: 2021-09-13 Revised: 2021-10-31 Accepted: 2021-11-04 Published: 2022-01-01
  • Contact: Jun Zhang E-mail:zhang6347@163.com;ycs@dlut.edu.cn

Abstract:

Wigner–Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity. We present the uncertainty principle for two successive projective measurements in terms of Wigner–Yanase skew information based on a single quantum system. It could capture the incompatibility of the observables, i.e. the lower bound can be nontrivial for the observables that are incompatible with the state of the quantum system. Furthermore, the lower bound is also constrained by the quantum Fisher information. In addition, we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state, respectively.

Key words: quantum uncertainty relation, successive measurements, Wigner–Yanase skew information