Scrambling and decoding the charged quantum information

Abstract

Some deep conjectures about quantum gravity are closely related to the role of symmetries in the gravitational background, especially for quantum black holes. In this paper, we systematically study the theory of quantum information for a charged, chaotic system. We show how the quantum information in the whole system has been represented by its charge sectors, using the theory of quantum chaos and quantum error correction, with concrete examples in the context of the complex SYK model. We discuss possible implications for black hole thought experiments and conjectures about quantum gravity in the dynamical setup. We believe this work will have potential applications from theories of quantum gravity to quantum simulation in quantum devices.

arXiv comment62 pages, many figures, theorems and remarks. v2: mainly correct errors and typos. v3: give improvements about presentations and references; remove and add some discussions

References in corpus (83)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• A bound on chaos
• 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
• On the Geometry of the String Landscape and the Swampland
• Fast Scramblers
• Causality, Analyticity and an IR Obstruction to UV Completion
• Replica Wormholes and the Entropy of Hawking Radiation
• Symmetries and Strings in Field Theory and Gravity
• Topological phases of fermions in one dimension
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
• Bulk Locality and Quantum Error Correction in AdS/CFT
• Soft Hair on Black Holes
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Operator Spreading in Random Unitary Circuits
• Chaos in quantum channels
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• The Anthropic Landscape of String Theory
• Group Equivariant Convolutional Networks
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Traversable Wormholes via a Double Trace Deformation
• The String Landscape and the Swampland
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Chaos and complexity by design
• Theta, Time Reversal, and Temperature
• Restrictions on Transversal Encoded Quantum Gate Sets
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Towards the fast scrambling conjecture
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Diving into traversable wormholes
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
• Quantum conditional mutual information and approximate Markov chains
• Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture
• Chaos, Complexity, and Random Matrices
• Naturalness and the Weak Gravity Conjecture
• Higher-order corrections to mass-charge relation of extremal black holes
• Constraints on symmetry from holography
• Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States
• The statistical mechanics of near-extremal black holes
• From Navier-Stokes To Einstein
• Notes on the complex Sachdev-Ye-Kitaev model
• Gauge Equivariant Convolutional Networks and the Icosahedral CNN
• Proof of the Weak Gravity Conjecture from Black Hole Entropy
• Carving out OPE space and precise $O(2)$ model critical exponents
• Spectral form factors and late time quantum chaos
• $T\bar{T}$ and EE, with implications for (A)dS subregion encodings
• Disentangling Scrambling and Decoherence via Quantum Teleportation
• Universal low temperature theory of charged black holes with AdS${}_2$ horizons
• Evidence for an Electrifying Violation of Cosmic Censorship
• A Holographic Derivation of the Weak Gravity Conjecture
• Renyi generalizations of the conditional quantum mutual information
• A Random Unitary Circuit Model for Black Hole Evaporation
• Efficient decoding for the Hayden-Preskill protocol
• Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution
• Symbolic integration with respect to the Haar measure on the unitary group
• Entropy Bounds on Effective Field Theory from Rotating Dyonic Black Holes
• The ghost in the radiation: Robust encodings of the black hole interior
• Trouble For Remnants
• Recovering quantum gates from few average gate fidelities
• Living on the Edge: A Toy Model for Holographic Reconstruction of Algebras with Centers
• Code properties from holographic geometries
• Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit
• Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments
• Matrix ensembles with global symmetries and 't Hooft anomalies from 2d gauge theory
• Weingarten calculus for matrix ensembles associated with compact symmetric spaces
• Scaling the semidefinite program solver SDPB
• Spectral decoupling in many-body quantum chaos
• Soft mode and interior operator in Hayden-Preskill thought experiment
• Towards holography via quantum source-channel codes
• RTNI - A symbolic integrator for Haar-random tensor networks
• Observer-dependent black hole interior from operator collision
• Operator growth in random quantum circuits with symmetry
• Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality
• Swiveled Rényi entropies
• Note on global symmetry and SYK model
• Horizons Protect Church-Turing

Cited by in corpus (19)

• A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance
• Representation Learning via Quantum Neural Tangent Kernels
• Quantum simulation of quantum field theories as quantum chemistry
• Near-optimal covariant quantum error-correcting codes from random unitaries with symmetries
• Toward simulating Superstring/M-theory on a quantum computer
• Black holes as clouded mirrors: the Hayden-Preskill protocol with symmetry
• Topological violation of global symmetries in quantum gravity
• Approximate symmetries and quantum error correction
• Universal limitation of quantum information recovery: symmetry versus coherence
• Estimating the randomness of quantum circuit ensembles up to 50 qubits
• Quantum error correction and large $N$
• Laziness, Barren Plateau, and Noise in Machine Learning
• Designs from Local Random Quantum Circuits with SU(d) Symmetry
• Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU($d$) Symmetry
• Hayden-Preskill Recovery in Hamiltonian Systems
• Charge-conserving unitaries typically generate optimal covariant quantum error-correcting codes
• Approximate quantum error correction, covariance symmetry, and their relation
• SU(d)-Symmetric Random Unitaries: Quantum Scrambling, Error Correction, and Machine Learning
• Dynamical transition in controllable quantum neural networks with large depth