TY - JOUR
T1 - A strengthened data processing inequality for the Belavkin-Staszewski relative entropy
AU - Bluhm, Andreas
AU - Capel, Ángela
PY - 2020/3/1
Y1 - 2020/3/1
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
SN - 0129-055X
JO - Reviews in Mathematical Physics
JF - Reviews in Mathematical Physics
ER -