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arXiv · 1904.10768

A strengthened data processing inequality for the Belavkin-Staszewski relative entropy

Andreas Bluhm·Angela Capel
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Abstract

In this work, we provide a strengthening of the data processing inequality for the relative entropy introduced by Belavkin and Staszewski (BS-entropy). This extends previous results by Carlen and Vershynina for the relative entropy and other standard $f$-divergences. To this end, we provide two new equivalent conditions for the equality case of the data processing inequality for the BS-entropy. Subsequently, we extend our result to a larger class of maximal $f$-divergences. Here, we first focus on quantum channels which are conditional expectations onto subalgebras and use the Stinespring dilation to lift our results to arbitrary quantum channels.

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Andreas Bluhm, Angela Capel. 2019-04-24. A strengthened data processing inequality for the Belavkin-Staszewski relative entropy. https://doi.org/10.1142/s0129055x20500051

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