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

authors

  • Bluhm, Andreas
  • CAPEL CUEVAS, ANGELA

publication date

  • March 2020

issue

  • 2

volume

  • 32

International Standard Serial Number (ISSN)

  • 0129-055X

Electronic International Standard Serial Number (EISSN)

  • 1793-6659

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.

keywords

  • bs-entropy; data processing inequality; maximal f-divergences