Letters in Mathematical Physics

, Volume 53, Issue 3, pp 243–251 | Cite as

Quantum Fisher Information and Uncertainty Relations

  • Shunlong Luo


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 equation quantum Fisher information quantum measurement uncertainty relations 


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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

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