# Causal Density Matrices

## TL;DR

This paper introduces the causal density matrix, a new quantum field theory construct derived from correlator singularities, which characterizes holographic dual causal geometries and reveals quantum error correction features.

## Contribution

It defines the causal density matrix and demonstrates its role in identifying holographic causal geometries, extending the framework beyond AdS/CFT.

## Key findings

- Causal density matrices characterize holographic causal geometries.
- Dual geometries exhibit quantum error correction features.
- Formalism applicable beyond AdS/CFT and gravity/QFT.

## Abstract

We define a new construct in quantum field theory - the causal density matrix - obtained from the singularity structure of correlators of local operators. This object provides a necessary and sufficient condition for a quantum field theory state to have a holographic semiclassical dual causal geometry. By exploiting the causal density matrix, we find that these dual causal geometries quite generally (even away from AdS/CFT) exhibit features of quantum error correction. Within AdS/CFT, we argue that the "reduced" causal density matrix is the natural dual to the causal wedge. Our formalism is very well-suited to generalizations of holography beyond AdS/CFT or even gravity/QFT.