Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2310.16988

Information recovery in the Hayden-Preskill protocol

Bartłomiej Czech, Sirui Shuai, Haifeng Tang

Published Oct 25, 2023• 0 citations
arXivHTMLPDF

Abstract

We revisit information retrieval from evaporating black holes in the Hayden-Preskill protocol, treating the black hole dynamics as Haar-random. We compute, down to the first exponentially suppressed terms, all integer-indexed Rényi mutual informations between a black hole, its radiation, and a reference that catalogues Alice's diaries. We find that dropping a diary into a young black hole effectively delays the Page time. We also compute the radiation : diary reflected Rényi entropies, and identify a technical reason why they cannot be continued to the reflected entropy by the replica trick.

DOI
10.48550/arxiv.2310.16988

Related papers

Entropies and reflected entropies in the Hayden-Preskill protocol

Bartłomiej Czech, Sirui Shuai, Haifeng Tang

A bstract We revisit information retrieval from evaporating black holes in the Hayden-Preskill protocol, treating the black hole dynamics as Haar-random. We compute, down to the first exponentially suppressed terms, all integer-indexed Rényi mutual informations between a black hole, its radiation, and a reference that catalogues Alice’s diaries. We find that dropping a diary into a young black hole effectively delays the Page time. We also compute the radiation: diary reflected Rényi entropies, and identify a technical reason why they cannot be continued to the reflected entropy by the replica trick.

Journal of High Energy Physics•Feb 7, 2024•4 citations

Information retrieval from Hawking radiation in the non-isometric model of black hole interior: theory and quantum simulations

Ran Li, Xuanhua Wang, Kun Zhang +1 more

The non-isometric holographic model of the black hole interior stands out as a potential resolution of the long-standing black hole information puzzle since it remedies the friction between the effective calculation and the microscopic description. In this study, combining the final-state projection model, the non-isometric model of black hole interior and Hayden-Preskill thought experiment, we investigate the information recovery from decoding Hawking radiation and demonstrate the emergence of the Page time in this setup. We incorporate the effective modes into the scrambling inside the horizon, which are usually disregarded in Hayden-Preskill protocols, and show that the Page time can be identified as the transition of information transmission channels from the EPR projection to the local projections. This offers a new perspective on the Page time. We compute the decoupling condition under which retrieving information is feasible and show that this model computes the black hole entropy consistent with the quantum extremal surface calculation. Assuming the full knowledge of the dynamics of the black hole interior, we show how Yoshida-Kitaev decoding strategy can be employed in the modified Hayden-Preskill protocol. Furthermore, we perform experimental tests of both probabilistic and Grover's search decoding strategies on the 7-qubit IBM quantum processors to validate our analytical findings and confirm the feasibility of retrieving information in the non-isometric model. This study would stimulate more interests to explore black hole information problem on the quantum processors.

arXiv:2307.01454•Jul 4, 2023•0 citations

Information retrieval from Hawking radiation in the non-isometric model of black hole interior: Theory and quantum simulation

Ran Li, Xuanhua Wang, Kun Zhang +1 more

The nonisometric holographic model of the black hole interior stands out as a potential resolution of the long-standing black hole information puzzle since it remedies the friction between the effective calculation and the microscopic description. In this study, combining the final-state projection model, the nonisometric model of black hole interior, and Hayden-Preskill thought experiment, we investigate the information recovery from decoding Hawking radiation and demonstrate the emergence of the Page time in this setup. We incorporate the effective modes into the scrambling inside the horizon, which are usually disregarded in Hayden-Preskill protocols, and show that the Page time can be identified as the transition of information transmission channels from the EPR projection to the local projections. This offers a new perspective on the Page time. We compute the decoupling condition under which retrieving information is feasible and show that this model computes the black hole entropy consistent with the quantum extremal surface calculation. Assuming the full knowledge of the dynamics of the black hole interior, we show how Yoshida-Kitaev decoding strategy can be employed in the modified Hayden-Preskill protocol. Furthermore, we perform experimental tests of both probabilistic and Grover’s search decoding strategies on the seven-qubit IBM quantum processors to validate our analytical findings and confirm the feasibility of retrieving information in the nonisometric model. This study would stimulate more interest to explore black hole information problem on the quantum processors. Published by the American Physical Society 2024

Physical review. D/Physical review. D.•Feb 5, 2024•4 citations

Demonstration of the Hayden-Preskill Protocol via Mutual Information

Jeong-Myeong Bae, Subeom Kang, Dong-han Yeom +1 more

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 ⋃ 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:1907.13290•Journal of the Korean Physical Society•Dec 1, 2019•2 citations

Entanglement asymmetry in the Hayden-Preskill protocol

Hui-Huang Chen, Zi-Jun Tang

In this paper, we consider the time evolution of entanglement asymmetry of the black hole radiation in the Hayden-Preskill thought experiment. We assume the black hole is initially in a mixed state since it is entangled with the early radiation. Alice throws a diary maximally entangled with a reference system into the black hole. After the black hole has absorbed the diary, Bob tries to recover the information that Alice thought should be destroyed by the black hole. In this protocol, we found that a U ( 1 ) symmetry of the radiation emerges before a certain transition time (the time when the vanishing entanglement asymmetry begins to grow). This emergent symmetry is exact in the thermodynamic limit and can be characterized by the vanishing entanglement asymmetry of the radiation. The transition time depends on the initial entropy and the size of the diary. What is more, when the initial state of the black hole is maximally mixed, this emergent symmetry survives during the whole procedure of the black hole radiation. We successfully explained this novel phenomenon using the decoupling inequality.

arXiv:2411.17695•Physical review. D/Physical review. D.•Mar 3, 2025•8 citations

Mixed-state entanglement and information recovery in thermalized states and evaporating black holes

Shreya Vardhan, Jonah Kudler-Flam, Hassan Shapourian +1 more

We study the universal behavior of quantum information-theoretic quantities in thermalized isolated quantum many-body systems and evaporating black holes. In particular, we study a genuine mixed-state entanglement measure called the logarithmic negativity, other correlation measures including the Renyi negativities and the mutual information, and a signature of multipartite entanglement called the reflected entropy. We also probe the feasibility of recovering quantum information from subsystems of a thermalized quantum many-body system or from the radiation of an evaporating black hole, using quantities such as relative entropy and Petz map fidelity. A recently developed technique called the equilibrium approximation allows us to probe these quantities at finite temperature. We find striking qualitative differences from the infinite temperature case, which has been the topic of previous studies using Haar-random states. In particular, we find regimes where the logarithmic negativity is extensive but the mutual information is sub-extensive, indicating a large amount of undistillable, bound entanglement in thermalized states. For evaporating black holes at finite temperature, both the logarithmic negativity and the Petz map fidelity reveal an important new time scale $t_b$, which is earlier than the Page time $t_p$ by a finite fraction of the total evaporation time. We find that $t_b$, as opposed to $t_p$, is the time scale at which quantum entanglement between different parts of the radiation becomes extensive, and the fidelity of information recovery for a large diary thrown into the black hole starts to grow.

arXiv:2112.00020•Nov 30, 2021•0 citations
We revisit information retrieval from evaporating black holes in the Hayden-Preskill protocol, treating the black hole dynamics as Haar-random. We compute, down to the first exponentially suppressed terms, all integer-indexed Rényi mutual informations between a black hole, its radiation, and a reference that catalogues Alice's diaries. We find that dropping a diary into a young black hole effectively delays the Page time. We also compute the radiation : diary reflected Rényi entropies, and identify a technical reason why they cannot be continued to the reflected entropy by the replica trick.
A bstract We revisit information retrieval from evaporating black holes in the Hayden-Preskill protocol, treating the black hole dynamics as Haar-random. We compute, down to the first exponentially suppressed terms, all integer-indexed Rényi mutual informations between a black hole, its radiation, and a reference that catalogues Alice’s diaries. We find that dropping a diary into a young black hole effectively delays the Page time. We also compute the radiation: diary reflected Rényi entropies, and identify a technical reason why they cannot be continued to the reflected entropy by the replica trick.
The non-isometric holographic model of the black hole interior stands out as a potential resolution of the long-standing black hole information puzzle since it remedies the friction between the effective calculation and the microscopic description. In this study, combining the final-state projection model, the non-isometric model of black hole interior and Hayden-Preskill thought experiment, we investigate the information recovery from decoding Hawking radiation and demonstrate the emergence of the Page time in this setup. We incorporate the effective modes into the scrambling inside the horizon, which are usually disregarded in Hayden-Preskill protocols, and show that the Page time can be identified as the transition of information transmission channels from the EPR projection to the local projections. This offers a new perspective on the Page time. We compute the decoupling condition under which retrieving information is feasible and show that this model computes the black hole entropy consistent with the quantum extremal surface calculation. Assuming the full knowledge of the dynamics of the black hole interior, we show how Yoshida-Kitaev decoding strategy can be employed in the modified Hayden-Preskill protocol. Furthermore, we perform experimental tests of both probabilistic and Grover's search decoding strategies on the 7-qubit IBM quantum processors to validate our analytical findings and confirm the feasibility of retrieving information in the non-isometric model. This study would stimulate more interests to explore black hole information problem on the quantum processors.
The nonisometric holographic model of the black hole interior stands out as a potential resolution of the long-standing black hole information puzzle since it remedies the friction between the effective calculation and the microscopic description. In this study, combining the final-state projection model, the nonisometric model of black hole interior, and Hayden-Preskill thought experiment, we investigate the information recovery from decoding Hawking radiation and demonstrate the emergence of the Page time in this setup. We incorporate the effective modes into the scrambling inside the horizon, which are usually disregarded in Hayden-Preskill protocols, and show that the Page time can be identified as the transition of information transmission channels from the EPR projection to the local projections. This offers a new perspective on the Page time. We compute the decoupling condition under which retrieving information is feasible and show that this model computes the black hole entropy consistent with the quantum extremal surface calculation. Assuming the full knowledge of the dynamics of the black hole interior, we show how Yoshida-Kitaev decoding strategy can be employed in the modified Hayden-Preskill protocol. Furthermore, we perform experimental tests of both probabilistic and Grover’s search decoding strategies on the seven-qubit IBM quantum processors to validate our analytical findings and confirm the feasibility of retrieving information in the nonisometric model. This study would stimulate more interest to explore black hole information problem on the quantum processors. Published by the American Physical Society 2024
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 ⋃ 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.
In this paper, we consider the time evolution of entanglement asymmetry of the black hole radiation in the Hayden-Preskill thought experiment. We assume the black hole is initially in a mixed state since it is entangled with the early radiation. Alice throws a diary maximally entangled with a reference system into the black hole. After the black hole has absorbed the diary, Bob tries to recover the information that Alice thought should be destroyed by the black hole. In this protocol, we found that a U ( 1 ) symmetry of the radiation emerges before a certain transition time (the time when the vanishing entanglement asymmetry begins to grow). This emergent symmetry is exact in the thermodynamic limit and can be characterized by the vanishing entanglement asymmetry of the radiation. The transition time depends on the initial entropy and the size of the diary. What is more, when the initial state of the black hole is maximally mixed, this emergent symmetry survives during the whole procedure of the black hole radiation. We successfully explained this novel phenomenon using the decoupling inequality.
We study the universal behavior of quantum information-theoretic quantities in thermalized isolated quantum many-body systems and evaporating black holes. In particular, we study a genuine mixed-state entanglement measure called the logarithmic negativity, other correlation measures including the Renyi negativities and the mutual information, and a signature of multipartite entanglement called the reflected entropy. We also probe the feasibility of recovering quantum information from subsystems of a thermalized quantum many-body system or from the radiation of an evaporating black hole, using quantities such as relative entropy and Petz map fidelity. A recently developed technique called the equilibrium approximation allows us to probe these quantities at finite temperature. We find striking qualitative differences from the infinite temperature case, which has been the topic of previous studies using Haar-random states. In particular, we find regimes where the logarithmic negativity is extensive but the mutual information is sub-extensive, indicating a large amount of undistillable, bound entanglement in thermalized states. For evaporating black holes at finite temperature, both the logarithmic negativity and the Petz map fidelity reveal an important new time scale tbt_btb​, which is earlier than the Page time tpt_ptp​ by a finite fraction of the total evaporation time. We find that tbt_btb​, as opposed to tpt_ptp​, is the time scale at which quantum entanglement between different parts of the radiation becomes extensive, and the fidelity of information recovery for a large diary thrown into the black hole starts to grow.