Letters in Mathematical Physics

, Volume 107, Issue 6, pp 1131–1155 | Cite as

The minimum Rényi entropy output of a quantum channel is locally additive

  • Gilad Gour
  • Todd Kemp


We show that the minimum Rényi entropy output of a quantum channel is locally additive for Rényi parameter \(\alpha >1\). While our work extends the results of Gour and Friedland (IEEE Trans. Inf. Theory 59(1):603, 2012) (in which local additivity was proven for \(\alpha =1\)), it is based on several new techniques that incorporate the multiplicative nature of \(\ell _p\)-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the Rényi additivity conjectures exhibit purely global effects of quantum channels. Interestingly, the approach presented here cannot be extended to Rényi entropies with parameter \(\alpha <1\).


Quantum information Entropy output Rényi entroy Additivity conjecture 

Mathematics Subject Classification

81P45 94A17 



We extend thanks to Mark Girard for many stimulating discussions on topics that are closely related to this work.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Institute for Quantum Science and TechnologyUniversity of CalgaryCalgaryCanada
  2. 2.Department of MathematicsUniversity of CaliforniaSan DiegoUSA

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