Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance

Published

Journal Article

© 2019 Author(s). We study the entropy production of the sandwiched Rényi divergence under the primitive Lindblad equation with Gel'fand-Naimark-Segal-detailed balance. We prove that the Lindblad equation can be identified as the gradient flow of the sandwiched Rényi divergence of any order α ∈ (0, ∞). This extends a previous result by Carlen and Maas [J. Funct. Anal. 273(5), 1810-1869 (2017)] for the quantum relative entropy (i.e., α = 1). Moreover, we show that the sandwiched Rényi divergence of any order α ∈ (0, ∞) decays exponentially fast under the time evolution of such a Lindblad equation.

Full Text

Duke Authors

Cited Authors

  • Cao, Y; Lu, J; Lu, Y

Published Date

  • May 1, 2019

Published In

Volume / Issue

  • 60 / 5

International Standard Serial Number (ISSN)

  • 0022-2488

Digital Object Identifier (DOI)

  • 10.1063/1.5083065

Citation Source

  • Scopus