2020/11/30 by Sam Cree, Jonathan Sorce · 1 citation
Physics and Astronomy · Mathematics · #quant-ph #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8121/ac5648
13 pages + 2 pages appendices; v2 contains some small corrections, additional pedagogical explanations, and is published in J. Phys. A: Math. Theor (2022)
arxiv created 2022/02/19 · arxiv updated 2022/02/22
The data processing inequality (DPI) is a scalar inequality satisfied by distinguishability measures on density matrices. For some distinguishability measures, saturation of the scalar DPI implies an operator equation relating the arguments of the measure. These results are typically derived using functional analytic techniques. In a complementary approach, we use geometric techniques to derive a formula that gives an operator equation from DPI saturation for any distinguishability measure; moreover, for a broad class of distinguishability measures, the derived operator equation is sufficient to imply saturation as well. Our operator equation coincides with known results for the sandwiched Rényi relative entropies, and gives new results for α-z Rényi relative entropies and a family of of quantum f-divergences, which we compute explicitly.