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Random Pure Gaussian States and Hawking Radiation
Erik Aurell1, Lucas Hackl2,3, Paweł Horodecki4,5
1<a href="https://ror.org/026vcq606">KTH-Royal Institute of Technology</a>, Alba Nova University Center, SE-106 91 Stockholm, Sweden.
Physical Review Letters
|August 23, 2024
Summary
Black holes evaporate via Hawking radiation, requiring entanglement for a pure state. This study finds minimal entanglement is needed, suggesting unitarity restoration doesn't rely on significant quantum entanglement between Hawking modes.
Area of Science:
- Quantum Gravity
- Black Hole Thermodynamics
- Quantum Information Theory
Background:
- Black holes are theorized to evaporate through Hawking radiation.
- Maintaining a pure quantum state during evaporation necessitates entanglement between radiation modes.
- Quantifying this entanglement has been a significant challenge.
Purpose of the Study:
- To develop a new theoretical framework for estimating the minimum entanglement in Hawking radiation.
- To analyze the role of entanglement in restoring black hole unitarity.
- To provide general expressions for mode-mode correlations in pure, Gaussian states.
Main Methods:
- Developed a novel theory of constrained random symplectic transformations.
- Assumed a pure and Gaussian total state with given marginals.
- Computed mode-mode correlations to bound mode-mode entanglement.
Main Results:
- Entanglement is strongly suppressed in thinly populated modes (high-frequency or late-time).
- Highly populated modes (early-time, low-frequency) show suppressed entanglement despite strong correlations.
- Unitarity restoration does not require significant entanglement between Hawking radiation modes.
Conclusions:
- The study establishes that significant quantum entanglement is not essential for restoring unitarity in black hole evaporation.
- The developed methods offer exact expressions for correlation distributions in pure, Gaussian states, with potential applications beyond black hole physics.
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