Gravitational back-reaction is magical
arXiv:2403.07056 · doi:10.1103/z3vr-w5c5
Abstract
We study the interplay between magic and entanglement in quantum many-body systems. We show that non-local magic, which is supported by the quantum correlations is lower bounded by the non-flatness of entanglement spectrum and upper bounded by the amount of entanglement in the system. We then argue that a smoothed version of non-local magic bounds the hardness of classical simulations for incompressible states. In conformal field theories, we conjecture that the non-local magic should scale linearly with entanglement entropy but sublinearly when an approximation of the state is allowed. We support the conjectures using both analytical arguments based on unitary distillation and numerical data from an Ising CFT. If the CFT has a holographic dual, then we prove that the non-local magic vanishes if and only if there is no gravitational back-reaction. Furthermore, we show that non-local magic is approximately equal to the rate of change of the minimal surface area in response to the change of cosmic brane tension in the bulk.
39 pages, 21 figures; Updated version to match journal submission
References in corpus (99)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Gaussian Quantum Information
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- A Covariant Holographic Entanglement Entropy Proposal
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Improved Simulation of Stabilizer Circuits
- Black Holes: Complementarity or Firewalls?
- Cool horizons for entangled black holes
- Generalized gravitational entropy
- Building up spacetime with quantum entanglement
- Quantum corrections to holographic entanglement entropy
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Time Evolution of Entanglement Entropy from Black Hole Interiors
- Operator Spreading in Random Unitary Circuits
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Chaos in quantum channels
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- The Resource Theory of Stabilizer Computation
- Holographic duality from random tensor networks
- Gravitation from Entanglement in Holographic CFTs
- Entanglement spectrum in one-dimensional systems
- The Ryu-Takayanagi Formula from Quantum Error Correction
- Relative Entropy and Holography
- The Gravity Dual of Renyi Entropy
- Improved classical simulation of quantum circuits dominated by Clifford gates
- Entanglement Equilibrium and the Einstein Equation
- Bipartite entanglement and entropic boundary law in lattice spin systems
- Trading classical and quantum computational resources
- Stabilizer Rényi entropy
- Simulation of quantum circuits by low-rank stabilizer decompositions
- Holographic Thermalization
- Entanglement entropy and entanglement spectrum of the Kitaev model
- Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
- Holographic Local Quenches and Entanglement Density
- Quantum Reverse Shannon Theorem
- Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
- Matchgates and classical simulation of quantum circuits
- Estimating outcome probabilities of quantum circuits using quasiprobabilities
- Flat entanglement spectra in fixed-area states of quantum gravity
- Holographic Renyi Entropy from Quantum Error Correction
- Bidirectional holographic codes and sub-AdS locality
- Conformal field theories are magical
- Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
- Quantum Chaos is Quantum
- Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
- Entanglement Wedge Cross Sections Require Tripartite Entanglement
- Entanglement of Local Operators in large N CFTs
- Stabilizer entropies are monotones for magic-state resource theory
- Magic-state resource theory for the ground state of the transverse-field Ising model
- Catalysis and activation of magic states in fault tolerant architectures
- Leading order corrections to the quantum extremal surface prescription
- Nuts and Bolts for Creating Space
- On the communication cost of entanglement transformations
- Nonstabilizerness via matrix product states in the Pauli basis
- Multipartite Entanglement in Stabilizer Tensor Networks
- Aspects of capacity of entanglement
- Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
- Phase transition in magic with random quantum circuits
- Nonstabilizerness determining the hardness of direct fidelity estimation
- Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
- Efficient quantum algorithms for stabilizer entropies
- Towards Bulk Metric Reconstruction from Extremal Area Variations
- Dynamical Magic Transitions in Monitored Clifford+T Circuits
- The Information Theoretic Interpretation of the Length of a Curve
- Holographic Reconstruction of General Bulk Surfaces
- Calderbank-Steane-Shor Holographic Quantum Error Correcting Codes
- A Holographic Proof of Rényi Entropic Inequalities
- Stabilizer entropy dynamics after a quantum quench
- Critical behaviors of non-stabilizerness in quantum spin chains
- Transitions in entanglement complexity in random quantum circuits by measurements
- All pure fermionic non-Gaussian states are magic states for matchgate computations
- Magic in generalized Rokhsar-Kivelson wavefunctions
- Characterization of an operational quantum resource in a critical many-body system
- Random tensor networks with nontrivial links
- Phase transition in Stabilizer Entropy and efficient purity estimation
- Equivalent Equations of Motion for Gravity and Entropy
- Approximate Bacon-Shor Code and Holography
- Holographic Renyi Entropy at High Energy Density
- Quantifying dynamical magic with completely stabilizer preserving operations as free
- Randomized benchmarking for qudit Clifford gates
- Holographic Codes from Hyperinvariant Tensor Networks
- Mana and thermalization: probing the feasibility of near-Clifford Hamiltonian simulation
- Computational power of matchgates with supplementary resources
- Building Bulk Geometry from the Tensor Radon Transform
- Entanglement and Stabilizer entropies of random bipartite pure quantum states
- Sharp Continuity Bounds for Entropy and Conditional Entropy
- The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories
- Stabilizer Testing and Magic Entropy via Quantum Fourier Analysis
- Holographic Tensor Networks with Bulk Gauge Symmetries
- Holographic Geometries of one-dimensional gapped quantum systems from Tensor Network States
- Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations
- Extracting randomness from magic quantum states
- Background independent tensor networks
- An Entropic Lens on Stabilizer States
- Understanding holographic error correction via unique algebras and atomic examples
- Unconditional quantum magic advantage in shallow circuit computation
- Clifford Orbits from Cayley Graph Quotients
- Bounding Entanglement Entropy with Clifford Double Cosets
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- Stabilizer Rényi Entropy and Conformal Field Theory
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- Computing quantum magic of state vectors
- An Exact Link between Nonlocal Nonstabilizerness and Operator Entanglement
- A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
- Local spreading of stabilizer Rényi entropy in a brickwork random Clifford circuit
- The Magic Barrier before Thermalization
- Optimal quantum reservoir learning in proximity to universality
- Spectral signatures of nonstabilizerness and criticality in infinite matrix product states
- On the stabilizer complexity of Hawking radiation
- Resource complexity of Symmetry Protected Topological phases