# Black Holes, Entanglement and Random Matrices

**Authors:** Vijay Balasubramanian, Micha Berkooz, Simon F. Ross, Joan Simon  
**arXiv:** [1404.6198](https://arxiv.org/abs/1404.6198)  
**Date:** 2014-04-24  
**Summary page:** https://www.summarizepaper.com/en/paper/1404.6198v3/

## Key points

- Authors explore relationship between strong quantum entanglement and semiclassical wormholes in AdS/CFT correspondence
- Strong entanglement doesn't always lead to wormhole formation but can create significant correlations between systems
- Novel approach using low-energy gravity probes as random operators to calculate correlators between entangled systems
- Presence of a wormhole depends on magnitude of correlations; large correlations possible even without a Lorentzian wormhole
- Random matrix model for probing operators provides insights into "seeing behind a horizon" and understanding black hole states through gravitational probes

## Summary

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In their paper "Black Holes, Entanglement and Random Matrices," authors Vijay Balasubramanian, Micha Berkooz, Simon F. Ross, and Joan Simon explore the relationship between strong quantum entanglement and the potential existence of semiclassical wormholes within the framework of the AdS/CFT correspondence. They present compelling evidence that while strong entanglement between Hilbert spaces does not necessarily lead to the formation of wormholes connecting corresponding geometric regions, it can still give rise to significant correlations between entangled systems. To investigate this further, the authors propose a novel approach by describing low-energy gravity probes as random operators acting on the space of black hole states. By utilizing this description, they are able to calculate correlators between entangled systems and demonstrate that the presence of a wormhole is contingent upon the magnitude of these correlations. Interestingly, they also argue that large correlations can exist even in scenarios where a Lorentzian wormhole is absent, highlighting the complexity of diagnosing spacetime connectedness based solely on the strength of entanglement. Moreover, their random matrix model for probing operators offers valuable insights into the challenging problem of "seeing behind a horizon," shedding light on how information about black hole states can be gleaned through gravitational probes. Overall, this study provides a nuanced perspective on the interplay between quantum entanglement, wormhole formation, and gravitational interactions in black hole systems within the context of theoretical physics.