# Unitarity of black hole evaporation in final-state projection models

**Authors:** Seth Lloyd, John Preskill  
**arXiv:** [1308.4209](https://arxiv.org/abs/1308.4209)  
**Date:** 2013-08-20  
**Summary page:** https://www.summarizepaper.com/en/paper/1308.4209v3/

## Key points

- Almheiri et al. addressed the compatibility issue between black hole evaporation and quantum entanglement monogamy
- The final-state projection model by Horowitz and Maldacena introduces concepts like cloning of quantum states and polygamous entanglement
- Achieving exact unitarity in the black hole S-matrix within this model requires finely tuned dynamics
- Deviations from unitarity are exponentially small relative to black hole entropy for generic final-state boundary conditions
- Observers inside black holes may not detect departures from standard quantum mechanics despite deviations from unitarity
- Conducting measurements within aged black holes could theoretically lead to causality-violating phenomena
- Deciphering Hawking radiation's information content poses significant computational challenges that may render causality violations unobservable in practice
- Lloyd and Preskill's investigation sheds light on circumventing core principles of standard quantum mechanics within a broader theory encompassing both quantum mechanics and gravity

## Summary

Keywords: 

In their study, Almheiri et al. highlighted a fundamental issue regarding the compatibility of black hole evaporation with the monogamy of quantum entanglement - a key principle in quantum mechanics. To address this challenge, the authors delved into the final-state projection model proposed by Horowitz and Maldacena for black hole evaporation. This model introduces intriguing concepts such as cloning of quantum states and polygamous entanglement, providing a framework to reconcile the unitarity of the evaporation process with the smoothness of the black hole event horizon. Upon closer examination, it became apparent that achieving exact unitarity in the black hole S-matrix within this model requires finely tuned dynamics. However, for a generic final-state boundary condition, any deviations from unitarity are shown to be exponentially small relative to the black hole entropy. Furthermore, observers situated inside black holes may not detect any departures from standard quantum mechanics despite these deviations. The researchers also explored potential implications of conducting measurements within aged black holes - which could theoretically lead to causality-violating phenomena. Nevertheless, they noted that deciphering Hawking radiation's information content might pose significant computational challenges that could render such causality violations unobservable in practice. Through their investigation of final-state projection models, Lloyd and Preskill shed light on how certain core principles of standard quantum mechanics could potentially be circumvented within a broader theory encompassing both quantum mechanics and gravity. Their work contributes valuable insights into the intricate interplay between quantum entanglement, unitarity in black hole evaporation processes, and the underlying fabric of spacetime itself.