Equality conditions of data processing inequality for α-z Rényi relative entropies

H. Zhang, Journal of Mathematical Physics 61 (2020).


Journal Article | Published | English

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Abstract
The α–z Rényi relative entropies are a two-parameter family of Rényi relative entropies that are quantum generalizations of the classical α-Rényi relative entropies. In the work [Adv. Math. 365, 107053 (2020)], we decided the full range of (α, z) for which the data processing inequality (DPI) is valid. In this paper, we give algebraic conditions for the equality in DPI. For the full range of parameters (α, z), we give necessary conditions and sufficient conditions. For most parameters, we give equivalent conditions. This generalizes and strengthens the results of Leditzky et al. [Lett. Math. Phys. 107, 61–80 (2017)].
Publishing Year
Date Published
2020-10-01
Journal Title
Journal of Mathematical Physics
Acknowledgement
This research was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 754411. The author would like to thank Anna Vershynina and Sarah Chehade for their helpful comments.
Volume
61
Issue
10
Article Number
102201
ISSN
IST-REx-ID

Cite this

Zhang H. Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics. 2020;61(10). doi:10.1063/5.0022787
Zhang, H. (2020). Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics, 61(10). https://doi.org/10.1063/5.0022787
Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z Rényi Relative Entropies.” Journal of Mathematical Physics 61, no. 10 (2020). https://doi.org/10.1063/5.0022787.
H. Zhang, “Equality conditions of data processing inequality for α-z Rényi relative entropies,” Journal of Mathematical Physics, vol. 61, no. 10, 2020.
Zhang H. 2020. Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics. 61(10).
Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z Rényi Relative Entropies.” Journal of Mathematical Physics, vol. 61, no. 10, 102201, AIP, 2020, doi:10.1063/5.0022787.
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