Geometric conditions for saturating the data processing inequality

Cree, Sam; Sorce, Jonathan

doi:10.1088/1751-8121/ac5648

Geometric conditions for saturating the data processing inequality

Journal Article · 03 March 2022 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8121/ac5648· OSTI ID:1979448

Cree, Sam ^[1];

OSTI

Abstract

The data processing inequality (DPI) is a scalar inequality satisfied by distinguishability measures on density matrices. For some distinguishability measures, saturation of thescalarDPI implies anoperatorequation 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 foranydistinguishability 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 forα-zRényi relative entropies and a family of of quantumf-divergences, which we compute explicitly.

Research Organization:: Univ. of California, Oakland, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0019380;

OSTI ID:: 1979448

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 13 Vol. 55; ISSN 1751-8113

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

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