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- Title
The minimum Rényi entropy output of a quantum channel is locally additive.
- Authors
Gour, Gilad; Kemp, Todd
- Abstract
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 $$\alpha <1$$ .
- Subjects
QUANTUM information theory; ENTROPY; ADDITIVITY (Mass spectrometry); QUANTUM communication; VON Neumann algebras
- Publication
Letters in Mathematical Physics, 2017, Vol 107, Issue 6, p1131
- ISSN
0377-9017
- Publication type
Article
- DOI
10.1007/s11005-016-0933-8