Quantum chaos and operator fidelity metric

Abstract

We show that the recently introduced operator fidelity metric provides a natural tool to investigate the cross-over to quantum chaotic behaviour. This metric is an information-theoretic measure of the global stability of a unitary evolution against perturbations. We use random matrix theory arguments to conjecture that the operator fidelity metric can be used as an "order parameter" to discriminates phases with regular behaviour from quantum chaotic ones. A numerical study of the onset of chaotic in the Dicke model is given in order to support the conjecture

4 pages, 3 figures

References in corpus (12)

• Ground state overlap and quantum phase transitions
• Quantum critical scaling of the geometric tensors
• Mixed-state fidelity and quantum criticality at finite temperature
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Ground-state fidelity in one-dimensional gapless model
• Bures metric over thermal state manifolds and quantum criticality
• Entanglement Across a Transition to Quantum Chaos
• Ground state fidelity and quantum phase transitions in free Fermi systems
• Operator fidelity susceptibility: an indicator of quantum criticality
• Operator fidelity susceptibility, decoherence and quantum criticality
• How complex is the quantum motion?
• Quantum Chernoff Bound metric for the XY model at finite temperature

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• Quantum metrology at level anti-crossing
• Deterministic generation of maximally discordant mixed states by dissipation
• Operator Quantum Geometric Tensor and Quantum Phase Transitions
• Sensitivity to perturbations and quantum phase transitions
• Quantum Geometric Tensor and Critical Metrology in the Anisotropic Dicke Model
• Fidelity and level correlations in the transition from regularity to chaos
• The transition to chaos of coupled oscillators: An operator fidelity susceptibility study
• Quantum speed limit for the OTOC from an open systems perspective