A team of researchers has proposed a potential solution to the black hole information puzzle through the nonisometric holographic model of the black hole interior. The model reconciles the friction between effective calculation and microscopic description. The team combined various models and experiments to investigate the recovery of information from decoding Hawking radiation. They also computed the decoupling condition under which retrieving information is feasible and validated their findings through experimental tests. The study could stimulate more interest in exploring the black hole information problem on quantum processors.
Introduction to the Nonisometric Model of Black Hole Interior
The nonisometric holographic model of the black hole interior is a potential solution to the longstanding black hole information puzzle. This model reconciles the friction between the effective calculation and the microscopic description. The study was conducted by Ran Li from the Department of Physics at Qufu Normal University, Xuanhua Wang from the Center for Theoretical Interdisciplinary Sciences at Wenzhou Institute, University of Chinese Academy of Sciences, Kun Zhang from the School of Physics at Northwest University, and Jin Wang from the Department of Chemistry and Department of Physics and Astronomy at The State University of New York at Stony Brook.
Theoretical Framework and Quantum Simulation
The researchers combined the final-state projection model, the nonisometric model of black hole interior, and the Hayden-Preskill thought experiment to investigate the recovery of information from decoding Hawking radiation. They demonstrated the emergence of the Page time in this setup. The Page time was identified as the transition of information transmission channels from the EPR projection to the local projections.
Decoupling Condition and Black Hole Entropy
The decoupling condition under which retrieving information is feasible was computed. The model was shown to compute the black hole entropy consistent with the quantum extremal surface calculation. The researchers assumed full knowledge of the dynamics of the black hole interior.
Yoshida-Kitaev Decoding Strategy
The Yoshida-Kitaev decoding strategy was employed in the modified Hayden-Preskill protocol. The researchers performed experimental tests of probabilistic and Grover’s search decoding strategies on the seven-qubit IBM quantum processors. The tests validated the analytical findings and confirmed the feasibility of retrieving information in the nonisometric model.
Implications and Future Directions
This study could stimulate more interest in exploring the black hole information problem on quantum processors. The nonisometric holographic model of encoding black hole interiors has inspired many interesting works. The researchers explored the possibility of treating the nonisometric mapping as a dual nonunitary dynamics inside the black hole and investigated the viability of decoding Hawking radiation and information recovery from the black hole.
The Hayden-Preskill Decoding Strategy
By studying the corresponding Hayden-Preskill decoding strategy, the researchers addressed the problem of the decoupling condition under which the information swallowed by the black hole can be recovered by decoding the Hawking radiation. This involved estimating the operator distance between the reduced density matrix of the black hole and reference system and the density matrix of their product state.
The Yoshida-Kitaev Decoding Strategies
Under the assumption that the black hole interior dynamics is known to the outside observer, the researchers discussed how the Yoshida-Kitaev decoding strategies can decode the Hawking radiation in the modified version of the Hayden-Preskill protocol. The corresponding decoding probability and the fidelity on average of the random unitary group were computed. The probability of the EPR projection demonstrated a phase transition behavior, allowing the identification of the Page time with the phase transition of information channels.
Published on February 5, 2024, in the Physical Review, the article “Information retrieval from Hawking radiation in the non-isometric model of black hole interior: Theory and quantum simulation” explores the theory and quantum simulation of information retrieval from Hawking radiation in the non-isometric model of black hole interior. The authors of this study are Ran Li, Xuanhua Wang, Kun Zhang, and Jin Wang.
