TY - JOUR

T1 - A strengthened data processing inequality for the Belavkin-Staszewski relative entropy

AU - Bluhm, Andreas

AU - Capel, Ángela

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - BS-entropy

KW - data processing inequality

KW - maximal f-divergences

UR - http://www.mendeley.com/research/strengthened-data-processing-inequality-belavkinstaszewski-relative-entropy

U2 - 10.1142/S0129055X20500051

DO - 10.1142/S0129055X20500051

M3 - Journal article

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

ER -