Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces
arXiv:2407.11822 · doi:10.21468/SciPostPhys.19.4.102
Abstract
Multipartite entanglement is a crucial resource for advancing quantum technologies, with considerable research efforts directed toward achieving its rapid and scalable generation. In this work, we derive an analytical expression for the time-averaged quantum Fisher information (QFI), enabling the detection of scalable multipartite entanglement dynamically generated by all quantum chaotic systems governed by Dyson's ensembles. Our approach integrates concepts of randomness and quantum chaos, demonstrating that the QFI is universally determined by the structure and dimension of the Krylov space that confines the chaotic dynamics. In particular, the QFI ranges from for qubits in the permutation-symmetric subspace (e.g. for chaotic kicked top models with long-range interactions), to when the dynamics extend over the full Hilbert space with or without bit reversal symmetry or parity symmetry (e.g. in chaotic models with short-range Ising-like interactions). In the former case, the QFI reveals multipartite entanglement among qubits and highlights the power of chaotic collective spin systems in generating scalable multipartite entanglement. Interestingly this result can be related to isotropic substructures in the Wigner distribution of chaotic states and demonstrates the efficacy of quantum chaos for Heisenberg-scaling quantum metrology. Finally, our general expression for the QFI agrees with that obtained for random states and, differently from out-of-time-order-correlators, it can also distinguish chaotic from integrable unstable spin dynamics.
23 pages, 6 figures
References in corpus (22)
- Quantum metrology from a quantum information science perspective
- Fisher Information and entanglement of non-Gaussian spin states
- Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
- Preparing random states and benchmarking with many-body quantum chaos
- Relating out-of-time-order correlations to entanglement via multiple-quantum coherences
- Scalable spin squeezing in a dipolar Rydberg atom array
- Quantum Dynamics in Krylov Space: Methods and Applications
- Bridging entanglement dynamics and chaos in semiclassical systems
- Entanglement, avoided crossings and quantum chaos in an Ising model with a tilted magnetic field
- The Lieb-Robinson light cone for power-law interactions
- Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
- Metrological Detection of Multipartite Entanglement from Young Diagrams
- Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
- Operator growth in the transverse-field Ising spin chain with integrability-breaking longitudinal field
- Strong quantum metrological limit from many-body physics
- Benchmarking Quantum Simulators using Ergodic Quantum Dynamics
- Efficient Generation of Spin Cat States
- Universal shot-noise limit for quantum metrology with local Hamiltonians
- Quantum delocalization on correlation landscape: The key to exponentially fast multipartite entanglement generation
- Symmetry classes in random matrix theory
- Complexity enriched dynamical phases for fermions on graphs
- Unlocking Heisenberg Sensitivity with Sequential Weak Measurement Preparation