Demonstration of the Hayden-Preskill protocol via mutual information

Abstract

We construct the Hayden-Preskill protocol by using a system of spin-1/2 particles and demonstrate information flows of this system which can mimic black holes. We first define an analogous black hole $A$ as a collection of such particles. Second, we take the particles from inside to outside the black hole to define an analogous system of Hawking radiation $B$ as outside particles. When the black hole and the radiation have the maximum entanglement at the Page time, we take an entangled pair system $C$ and $D$. The particles of $C$ fall into the black hole while their counterparts of $D$ remain outside. If we assume rapid mixing of the particle states in the black hole $A\cup C$, can the information of $C$ rapidly escape from the black hole like a mirror? We numerically show that if we turn on the rapid mixing in the black hole, the original information of $C$ rapidly escapes from the black hole to outside in the form of the mutual information between $B$ and $D$. On the other hand, if the mixing between $A$ and $C$ is not enough, the information escapes slowly. Hence, we explicitly demonstrate the original conjecture of Hayden and Preskill. We emphasize that enough mixing is an essential condition to make the Hayden-Preskill protocol functionally work.

arXiv comment12 pages, 4 figures

References in corpus (31)

• Average Entropy of a Subsystem
• Black Holes: Complementarity or Firewalls?
• Black holes as mirrors: quantum information in random subsystems
• Information in Black Hole Radiation
• The Stretched Horizon and Black Hole Complementarity
• An Apologia for Firewalls
• Time Dependence of Hawking Radiation Entropy
• Black Hole Remnants and the Information Loss Paradox
• The black hole final state
• Gedanken Experiments involving Black Holes
• The causal structure of dynamical charged black holes
• Information locking in black holes
• Is the firewall consistent?: Gedanken experiments on black hole complementarity and firewall proposal
• Why Aren't Black Holes Infinitely Produced?
• Constructing a counterexample to the black hole complementarity
• Semi-classical black holes with large N re-scaling and information loss problem
• Naked Black Hole Firewalls
• Entropy evolution of moving mirrors and the information loss problem
• Black hole complementarity and firewall in two dimensions
• Generalized Uncertainty Principle: Implications for Black Hole Complementarity
• Thin-shell bubbles and information loss problem in anti de Sitter background
• Thermal activation of thin-shells in anti-de Sitter black hole spacetime
• Entropy/information flux in Hawking radiation
• Entropy budget for Hawking evaporation
• Dynamics of magnetic shells and information loss problem
• Status report: black hole complementarity controversy
• Hawking radiation as instantons
• Black hole complementarity with local horizons and Horowitz-Maldacena's proposal
• How can we erase states inside a black hole?
• Page curves for tripartite systems
• Reviews and perspectives on black hole complementarity

Cited by in corpus (1)

• Before the Page time: maximum entanglements or the return of the monster?