Letters in Mathematical Physics

, Volume 53, Issue 3, pp 243–251

Quantum Fisher Information and Uncertainty Relations

  • Shunlong Luo

DOI: 10.1023/A:1011080128419

Cite this article as:
Luo, S. Letters in Mathematical Physics (2000) 53: 243. doi:10.1023/A:1011080128419


It is well known that the Cramér–Rao inequality places a lower bound for quantum Fisher information in terms of the variance of any quantum measurement. We establish an upper bound for quantum Fisher information of a parameterized family of density operators in terms of the variance of the generator. These two bounds together yield a generalization of the Heisenberg uncertainty relations from statistical estimation perspective.

von Neumann equationquantum Fisher informationquantum measurementuncertainty relations

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Shunlong Luo
    • 1
  1. 1.Institute of Applied Mathematics, Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijingP.R. China