Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal Entanglement Structure
arXiv:2210.14926 · doi:10.1103/PRXQuantum.5.010314
Abstract
Chaotic systems are highly sensitive to a small perturbation, and are ubiquitous throughout biological sciences, physical sciences and even social sciences. Taking this as the underlying principle, we construct an operational notion for quantum chaos. Namely, we demand that the future state of a many-body, isolated quantum system is sensitive to past multitime operations on a small subpart of that system. By `sensitive', we mean that the resultant states from two different perturbations cannot easily be transformed into each other. That is, the pertinent quantity is the complexity of the effect of the perturbation within the final state. From this intuitive metric, which we call the Butterfly Flutter Fidelity, we use the language of multitime quantum processes to identify a series of operational conditions on chaos, in particular the scaling of the spatiotemporal entanglement. Our criteria already contain the routine notions, as well as the well-known diagnostics for quantum chaos. This includes the Peres-Loschmidt Echo, Dynamical Entropy, Tripartite Mutual Information, and Local-Operator Entanglement. We hence present a unified framework for these existing diagnostics within a single structure. We also go on to quantify how several mechanisms lead to quantum chaos, such as evolution generated from random circuits. Our work paves the way to systematically study many-body dynamical phenomena like Many-Body Localization, measurement-induced phase transitions, and Floquet dynamics.
arXiv commentUpdated/condensed results and discussion. 18 + 7 pages, 7 figures
References in corpus (81)
- Decoherence, einselection, and the quantum origins of the classical
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Area laws for the entanglement entropy - a review
- Entanglement in quantum critical phenomena
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- A bound on chaos
- Black holes and the butterfly effect
- Black holes as mirrors: quantum information in random subsystems
- Entanglement renormalization
- Fast Scramblers
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Chaos in quantum channels
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Localized shocks
- Many-body localization: an introduction and selected topics
- Environment-independent decoherence rate in classically chaotic systems
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Quantum Computation as Geometry
- Quantum Many-Body Scars and Weak Breaking of Ergodicity
- Theoretical framework for quantum networks
- A Theory of Trotter Error
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Multiple Shocks
- Chaos and complexity by design
- Entropy scaling and simulability by Matrix Product States
- Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
- Quantum Circuits Architecture
- A Universal Operator Growth Hypothesis
- Non-Markovian quantum processes: complete framework and efficient characterisation
- Lieb-Robinson and the butterfly effect
- Most quantum states are too entangled to be useful as computational resources
- Operational Markov condition for quantum processes
- Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
- Quantum causal modelling
- Operator space entanglement entropy in transverse Ising chain
- Does scrambling equal chaos?
- Quantum stochastic processes and quantum non-Markovian phenomena
- Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
- The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
- Information Scrambling and Loschmidt Echo
- Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
- Fidelity Decay as an Efficient Indicator of Quantum Chaos
- Is efficiency of classical simulations of quantum dynamics related to integrability?
- Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
- Many body localization and thermalization: insights from the entanglement spectrum
- Causal and causally separable processes
- Quantum localization bounds Trotter errors in digital quantum simulation
- Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
- Are random pure states useful for quantum computation?
- Operator Space Entanglement Entropy in XY Spin Chains
- Measuring the Lyapunov exponent using quantum mechanics
- Quantum Chaos is Quantum
- Emergent irreversibility and entanglement spectrum statistics
- Nonuniversal Entanglement Level Statistics in Projection-driven Quantum Circuits
- When is a non-Markovian quantum process classical?
- Efficient unitary designs with nearly time-independent Hamiltonian dynamics
- Exponential speed-up with a single bit of quantum information: Testing the quantum butterfly effect
- An introduction to operational quantum dynamics
- Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories
- Scrambling is Necessary but Not Sufficient for Chaos
- Quantum Markov Order
- The Structure of Quantum Stochastic Processes with Finite Markov Order
- Classical quantum stochastic processes
- Speed limits and locality in many-body quantum dynamics
- Large Deviation Bounds for k-designs
- Superdensity Operators for Spacetime Quantum Mechanics
- Updating the Born rule
- Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
- Conformal field theory and the web of quantum chaos diagnostics
- Diffusion and operator entanglement spreading
- Quantum coherence as a signature of chaos
- Almost Markovian processes from closed dynamics
- Isospectral twirling and quantum chaos
- Genuine Multipartite Entanglement in Time
- Hidden non-Markovianity in open quantum systems
- Markovianization with approximate unitary designs
- Relaxation of Multitime Statistics in Quantum Systems
- Equilibration of Multitime Quantum Processes in Finite Time Intervals
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- Quantum Chaos and Coherence: Random Parametric Quantum Channels
- Adversarial Robustness Guarantees for Quantum Classifiers
- The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes
- Capturing long-range memory structures with tree-geometry process tensors
- What can unitary sequences tell us about multi-time physics?
- Understanding and utilizing the inner bonds of process tensors
- Decoherence of Histories: Chaotic Versus Integrable Systems
- Random Permutation Circuits Beyond Qubits are Quantum Chaotic
- Tensor Product Structure Geometry under Unitary Channels
- Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity
- Symmetry Properties of Quantum Dynamical Entropy
- Diagnosing chaos with projected ensembles of process tensors
- Long-time signatures of chaos in large atom-light frequency ratios Rabi model
- Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations