Quantum Information Processing

, Volume 15, Issue 6, pp 2639–2648 | Cite as

Sum uncertainty relations based on Wigner–Yanase skew information

  • Bin ChenEmail author
  • Shao-Ming Fei
  • Gui-Lu Long


We study sum uncertainty relations for arbitrary finite N quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial as long as the observables are mutually noncommutative. The relations among these new and existing uncertainty inequalities have been investigated. Detailed examples are presented.


Uncertainty relation Wigner–Yanase skew information Noncommuting observables 



We would like to thank Dr. Shu-Hao Wang for his helpful discussions and suggestions. This work is supported by the National Basic Research Program of China (2015CB921002), the National Natural Science Foundation of China Grant Nos. 11175094, 91221205, and 11275131.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.State Key Laboratory of Low-Dimensional Quantum Physics and Department of PhysicsTsinghua UniversityBeijingChina
  2. 2.Tsinghua National Laboratory for Information Science and TechnologyBeijingChina
  3. 3.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  4. 4.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany
  5. 5.Collaborative Innovation Center of Quantum MatterBeijingChina

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