Quantum chaos, randomness and universal scaling of entanglement in various Krylov spaces

Year: 2025

Authors: Shi HL., Smerzi A., Pezzè L.

Autors Affiliation: INO CNR & LENS, QSTAR, Largo Enr Fermi 2, I-50125 Florence, Italy.

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 N2/3 for N qubits in the permutation-symmetric subspace (e.g. for chaotic kicked top models with long-range interactions), to N when the dynamics extend over the full Hilbert space with or without bit reversal symmetry or parity symmetry (e.g. in chaotic models with shortrange Ising-like interactions). In the former case, the QFI reveals multipartite entanglement among N/3 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.

Journal/Review: SCIPOST PHYSICS

Volume: 19 (4)      Pages from: 102-1  to: 102-23

More Information: This work was supported by the European Commission through the H2020 QuantERA ERA-NET Cofund in Quantum Technologies project MENTA and received funding under Horizon Europe programme HORIZONCL4-2022-QUANTUM-02-SGA via the project 101113690 (PASQuanS2.1).
KeyWords: Body Approximation Methods; Statistical-theory; Solvable Model; Energy-levels; Symmetry Classes; Dynamics; Validity; States; Thermalization; Information
DOI: 10.21468/SciPostPhys.19.4.102