# Classical Spacetimes as Amplified Information in Holographic Quantum Theories

**Authors:** Yasunori Nomura, Pratik Rath, Nico Salzetta  
**arXiv:** [1705.06283](https://arxiv.org/abs/1705.06283)  
**Date:** 2017-05-17  
**Summary page:** https://www.summarizepaper.com/en/paper/1705.06283v4/

## Key points

- Classical spacetimes as amplified information in holographic quantum theories
- Classicalization of a quantum system involves amplification of information at the expense of reducing observables exponentially
- Geometry of spacetime represents the amplified information in quantum gravity
- Focus on bulk local semiclassical operators that probe the amplified information without disturbing it
- Bulk local operators correspond to logical operators acting on code subspaces in holographic theories
- Study how these operators can be realized in a holographic theory encompassing general spacetimes, including AdS/CFT as a special case
- First half: Investigation of what description of bulk physics is provided by a holographic state dual to a semiclassical spacetime, suggesting that it provides an exterior perspective while retaining some interior information when there is a quasi-static black hole enclosed by a holographic screen
- Second half: Exploration of how and when semiclassical descriptions emerge in holographic theories, finding that states representing semiclassical spacetimes are non-generic and require state-dependent semiclassical operators; use stabilizer formalism and tensor network models for illustration
- Discussion of potential implications for understanding black hole interiors based on the proposed framework

## Summary

In their paper "Classical Spacetimes as Amplified Information in Holographic Quantum Theories," Yasunori Nomura, Pratik Rath, and Nico Salzetta explore the concept of classical spacetimes as amplified information within the framework of holographic quantum gravity. They argue that classicalization of a quantum system involves amplification of information at the expense of reducing the number of observables exponentially. In the context of quantum gravity, they propose that the geometry of spacetime represents this amplified information. The authors focus on bulk local semiclassical operators, which probe the amplified information without disturbing it. These operators correspond to logical operators acting on code subspaces in holographic theories. By studying how these bulk local operators can be realized in a holographic theory encompassing general spacetimes (including AdS/CFT as a special case), they aim to deduce its consequences. The paper is divided into two parts. In the first half, the authors investigate what description of bulk physics is provided by a holographic state dual to a semiclassical spacetime. Specifically, they analyze which portion of the bulk can be reconstructed as spacetime within the holographic theory. Their analysis suggests that when a spacetime contains a quasi-static black hole enclosed by a holographic screen, the theory provides a description of physics from an exterior perspective while still retaining some interior information. In the second half, Nomura et al. delve into how and when a semiclassical description emerges in holographic theories. They find that states representing semiclassical spacetimes are non-generic in the holographic Hilbert space. If there exists a maximal number of independent microstates, semiclassical operators must be given state-dependently. To illustrate this point, they employ both stabilizer formalism and tensor network models. Additionally, the authors discuss possible implications for understanding black hole interiors based on their proposed framework. Overall, this paper contributes to our understanding of classical spacetimes as amplified information within holographic quantum theories and sheds light on several aspects such as:  (1)the description of bulk physics in holographic states; (2)the emergence of semiclassical descriptions; and (3)potential implications for black hole interiors.