Black holes as clouded mirrors: the Hayden-Preskill protocol with symmetry
arXiv:2007.00895 · doi:10.22331/q-2023-02-21-928
Abstract
The Hayden-Preskill protocol is a qubit-toy model of the black hole information paradox. Based on the assumption of scrambling, it was revealed that quantum information is instantly leaked out from the quantum many-body system that models a black hole. In this paper, we extend the protocol to the case where the system has symmetry and investigate how the symmetry affects the leakage of information. We especially focus on the conservation of the number of up-spins. Developing a partial decoupling approach, we first show that the symmetry induces a delay of leakage and an information remnant. We then clarify the physics behind them: the delay is characterized by thermodynamic properties of the system associated with the symmetry, and the information remnant is closely related to the symmetry-breaking of the initial state. These relations bridge the information leakage problem to macroscopic physics of quantum many-body systems and allow us to investigate the information leakage only in terms of physical properties of the system.
arXiv commentVer.1: 7 pages + Supplementary. Ver.2: short version (14 pages) + long version (47 pages). Presentation improved. Connection to thermodynamics is much more elaborated. Ver.3: Substantial update of presentation. 21 pages + 6 pages of appendices. Ver 4-7: improved. Ver 8: Published version
References in corpus (46)
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Comments on the Sachdev-Ye-Kitaev model
- Average Entropy of a Subsystem
- Black holes and the butterfly effect
- Black holes as mirrors: quantum information in random subsystems
- The String Landscape, Black Holes and Gravity as the Weakest Force
- Fast Scramblers
- Symmetries and Strings in Field Theory and Gravity
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Chaos in AdS holography
- Chaos in quantum channels
- Monogamy of entanglement and other correlations
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Quantum information can be negative
- Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
- Bekenstein-Hawking Entropy and Strange Metals
- Coding Theorem and Strong Converse for Quantum Channels
- Two-dimensional conformal field theory and the butterfly effect
- Chaos and complexity by design
- Towards the fast scrambling conjecture
- Aspects of generic entanglement
- Verified Quantum Information Scrambling
- Quantum Information Processing with Finite Resources -- Mathematical Foundations
- Local random quantum circuits are approximate polynomial-designs
- Quantum state merging and negative information
- The mother of all protocols: Restructuring quantum information's family tree
- Universal Charge Diffusion and the Butterfly Effect
- Constraints on symmetry from holography
- A decoupling approach to the quantum capacity
- One-shot decoupling
- Continuous symmetries and approximate quantum error correction
- Learning the Alpha-bits of Black Holes
- Efficient unitary designs with nearly time-independent Hamiltonian dynamics
- Restrictions on realizable unitary operations imposed by symmetry and locality
- Addendum to Fast Scramblers
- Efficient unitary designs with a system-size independent number of non-Clifford gates
- Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames
- Error Correction of Quantum Reference Frame Information
- Toy Models of Holographic Duality between local Hamiltonians
- Efficient Quantum Tensor Product Expanders and k-designs
- Near-optimal covariant quantum error-correcting codes from random unitaries with symmetries
- Soft mode and interior operator in Hayden-Preskill thought experiment
- Towards holography via quantum source-channel codes
- Scrambling and decoding the charged quantum information
- Complementarity, distillable secret key, and distillable entanglement
- One-Shot Randomized and Nonrandomized Partial Decoupling
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- Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
- Approximate symmetries and quantum error correction
- Unraveling the emergence of quantum state designs in systems with symmetry
- One-Shot Randomized and Nonrandomized Partial Decoupling
- Designs from Local Random Quantum Circuits with SU(d) Symmetry
- Theory of Quantum Circuits with Abelian Symmetries
- Unitary Designs of Symmetric Local Random Circuits
- Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
- Hayden-Preskill Recovery in Hamiltonian Systems
- Non-Clifford Cost of Random Unitaries
- Decoding general error correcting codes and the role of complementarity
- SU(d)-Symmetric Random Unitaries: Quantum Scrambling, Error Correction, and Machine Learning
- On Computational Complexity of Unitary and State Design Properties
- Explicit decoders using fixed-point amplitude amplification based on QSVT
- Synthesis of Energy-Conserving Quantum Circuits with XY interaction