
TL;DR
This paper explores the holographic duals of a broad family of information-theoretic divergences, providing explicit bulk expressions for various parameters and extending to arbitrary backgrounds and dimensions.
Contribution
It derives explicit bulk expressions for the holographic duals of the $ ext{α}$-$z$ divergences for specific parameter ranges, generalizing previous results.
Findings
Explicit bulk expressions for boundary divergences at second order in perturbation.
Applicability to arbitrary background states and dimensions.
Results depend on the equality of bulk and boundary modular flows.
Abstract
We study the holographic dual of a two parameter family of quantities known as the - divergences. Many familiar information theoretic quantities occur within this family, including the relative entropy, fidelity, and collision relative entropy. We find explicit bulk expressions for the boundary divergences to second order in a state perturbation whenever is an integer and , as well as when and . Our results apply for perturbations around an arbitrary background state and in any dimension, under the assumption of the equality of bulk and boundary modular flows.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
