Fidelity and Purity Decay in Weakly Coupled Composite Systems

Abstract

We study the stability of unitary quantum dynamics of composite systems (for example: central system + environment) with respect to weak interaction between the two parts. Unified theoretical formalism is applied to study different physical situations: (i) coherence of a forward evolution as measured by purity of the reduced density matrix, (ii) stability of time evolution with respect to small coupling between subsystems, and (iii) Loschmidt echo measuring dynamical irreversibility. Stability has been measured either by fidelity of pure states of a composite system, or by the so-called reduced fidelity of reduced density matrices within a subsystem. Rigorous inequality among fidelity, reduced-fidelity and purity is proved and a linear response theory is developed expressing these three quantities in terms of time correlation functions of the generator of interaction. The qualitatively different cases of regular (integrable) or mixing (chaotic in the classical limit) dynamics in each of the subsystems are discussed in detail. Theoretical results are demonstrated and confirmed in a numerical example of two coupled kicked tops.

21 pages, 12 eps figures

References in corpus (19)

• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• On general relation between quantum ergodicity and fidelity of quantum dynamics
• Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic Systems
• Stability of quantum motion and correlation decay
• Fidelity Decay as an Efficient Indicator of Quantum Chaos
• Sensitivity of Quantum Motion for Classically Chaotic Systems
• Measuring the Lyapunov exponent using quantum mechanics
• Decay of the Loschmidt Echo for quantum states with sub-Planck scale structures
• Decoherence as Decay of the Loschmidt Echo in a Lorentz Gas
• Saturation of the production of quantum entanglement between weakly coupled mapping systems in strongly chaotic region
• Can quantum chaos enhance stability of quantum computation?
• Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states
• Decoherence of spin echoes
• Coupled Map Networks as Communication Schemes
• Decoherence scenarios from micro- to macroscopic superpositions
• A random matrix approach to decoherence
• Sensitivity to perturbations in a quantum chaotic billiard
• Crossover of quantum Loschmidt echo from golden rule decay to perturbation-independent decay
• Decoherence in chaotic and integrable systems: A random matrix approach

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• Bridging entanglement dynamics and chaos in semiclassical systems
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• Semiclassical time-evolution of the reduced density matrix and dynamically assisted generation of entanglement for bipartite quantum systems
• Chaos and Complexity of quantum motion
• Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models
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• Global entangling properties of the coupled kicked tops
• Quantum ergodicity and entanglement in kicked coupled-tops
• Intrinsic Decoherence Dynamics in Smooth Hamiltonian Systems: Quantum-classical Correspondence
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• Lyapunov Generation of Entanglement and the Correspondence Principle
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• Quantum freeze of fidelity decay for a class of integrable dynamics
• Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit
• Unitary equilibration after a quantum quench of a thermal state
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• Entanglement dynamics for two interacting spins
• Generation of entanglement in regular systems
• Entanglement in the classical limit: quantum correlations from classical probabilities
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Quantum Reversibility and Echoes in Interacting Systems
• Entanglement in coupled kicked tops with chaotic dynamics
• Berry phase and fidelity susceptibility of the three-qubit Lipkin-Meshkov-Glick ground state
• Fidelity susceptibility of one-dimensional models with twisted boundary conditions
• Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study
• Estimating purity in terms of correlation functions
• Probing internal bath dynamics by a Rabi oscillator-based detector
• The Loschmidt echo in classically chaotic systems: Quantum chaos, irreversibility and decoherence
• Transition from pure-state to mixed-state entanglement by random scattering
• About Quantum Revivals, Quantum Fidelity, A semiclassical Approach
• The quantum fidelity for the time-dependent singular quantum oscillator
• Kraus decomposition for chaotic environments
• Quantum pathology of static internal imperfections in flawed quantum computers
• Dynamical aspects of quantum entanglement for coupled mapping systems
• Decoherence, relaxation and chaos in a kicked-spin ensemble
• Quantum Chaos: Reduced Density Matrix Fluctuations in Coupled Systems
• A Quantum Fidelity Study of the Anisotropic Next-Nearest-Neighbour Triangular Lattice Heisenberg Model
• Decoherence in regular systems
• Entanglement production in a chaotic quantum dot
• Linear dynamical entropy and free-independence for quantized maps on the torus