# Connecting Fisher information to bulk entanglement in holography

## TL;DR

This paper proposes a holographic dual of the Fisher information metric for mixed states in AdS/CFT, linking it to bulk volume and entanglement entropy corrections, advancing quantum information understanding in holography.

## Contribution

It introduces a holographic measure for the distance between mixed states, connecting Fisher information to bulk volume and quantum corrections in entanglement entropy.

## Key findings

- Fisher information metric relates to regularized bulk volume.
- Quantum corrections to Fisher information correspond to entanglement entropy corrections.
- The approach provides a new link between quantum information and holographic geometry.

## Abstract

In the context of relating AdS/CFT to quantum information theory, we propose a holographic dual of Fisher information metric for mixed states in the boundary field theory. This amounts to a holographic measure for the distance between two mixed quantum states. For a spherical subregion in the boundary we show that this is related to a particularly regularized volume enclosed by the Ryu-Takayanagi surface. We further argue that the quantum correction to the proposed Fisher information metric is related to the quantum correction to the boundary entanglement entropy. We discuss consequences of this connection.