Petz reconstruction in random tensor networks

TL;DR

This paper explores how Petz reconstruction maps can be used to recover bulk operators from boundary data in random tensor network models of holography, highlighting the role of the replica trick.

Contribution

It demonstrates the application of Petz reconstruction in random tensor networks and discusses distinctions between coarse-graining and random projections.

Findings

Petz reconstruction effectively retrieves bulk operators from boundary data.

The replica trick facilitates the implementation of Petz maps in tensor networks.

Insights into the differences between coarse-graining and random projections in holography.

Abstract

We illustrate the ideas of bulk reconstruction in the context of random tensor network toy models of holography. Specifically, we demonstrate how the Petz reconstruction map works to obtain bulk operators from the boundary data by exploiting the replica trick. We also take the opportunity to comment on the differences between coarse-graining and random projections.