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Quantum Information Processing

, Volume 14, Issue 6, pp 2227–2238 | Cite as

Uncertainty relations based on mutually unbiased measurements

  • Bin Chen
  • Shao-Ming Fei
Article

Abstract

We derive uncertainty relation inequalities according to the mutually unbiased measurements. Based on the calculation of the index of coincidence of probability distribution given by \(d+1\) MUMs on any density operator \(\rho \) in \({\mathbb {C}}^{d}\), both state-dependent and state-independent forms of lower entropic bounds are given. Furthermore, we formulate uncertainty relations for MUMs in terms of Rényi and Tsallis entropies.

Keywords

Uncertainty relations Mutually unbiased measurements  Index of coincidence Rényi and Tsallis entropies 

Notes

Acknowledgments

This work is supported by the NSFC under number 11275131.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  2. 2.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany

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