Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states

Abstract

We prove that the entanglement entropy of any pure initial state of a bipartite bosonic quantum system grows linearly in time with respect to the dynamics induced by any unstable quadratic Hamiltonian. The growth rate does not depend on the initial state and is equal to the sum of certain Lyapunov exponents of the corresponding classical dynamics. This paper generalizes the findings of [Bianchi et al., JHEP 2018, 25 (2018)], which proves the same result in the special case of Gaussian initial states. Our proof is based on a recent generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum systems [De Palma et al., arXiv:2105.05627]. This technique allows us to extend our result to generic mixed initial states, with the squashed entanglement providing the right generalization of the entanglement entropy. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems, including certain quantum field theory models.

arXiv comment31 pages, 4 figures, 1 table

References in corpus (61)

• Area laws for the entanglement entropy - a review
• A bound on chaos
• Towards the Theory of Reheating After Inflation
• Aspects of Holographic Entanglement Entropy
• Entropy and Area
• Entanglement entropy and conformal field theory
• Black holes and the butterfly effect
• Holographic Entanglement Entropy: An Overview
• Localized shocks
• Semiclassicality and Decoherence of Cosmological Perturbations
• Reheating in Inflationary Cosmology: Theory and Applications
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Nonperturbative Dynamics Of Reheating After Inflation: A Review
• Decoherence, Chaos, and the Second Law
• Entanglement and thermodynamics after a quantum quench in integrable systems
• "Squashed Entanglement" - An Additive Entanglement Measure
• Entanglement dynamics after quantum quenches in generic integrable systems
• Current status of the Dynamical Casimir Effect
• Faithful Squashed Entanglement
• On entanglement spreading in chaotic systems
• Parametric resonance in quantum field theory
• Entanglement Growth after a Global Quench in Free Scalar Field Theory
• Entropy of gravitons produced in the early Universe
• Geometry of variational methods: dynamics of closed quantum systems
• Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
• Entanglement of Distillation and Conditional Mutual Information
• Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
• The entropy power inequality for quantum systems
• Entanglement production in bosonic systems: Linear and logarithmic growth
• Quantum Entanglement and Conditional Information Transmission
• Entanglement entropy of squeezed vacua on a lattice
• Inflationary spectra and partially decohered distributions
• Fidelity of recovery, geometric squashed entanglement, and measurement recoverability
• Squashed entanglement, k-extendibility, quantum Markov chains, and recovery maps
• Reheating after Supercooling in the Chiral Phase Transition
• A generalization of the Entropy Power Inequality to Bosonic Quantum Systems
• Relative entropy and squashed entanglement
• Rényi squashed entanglement, discord, and relative entropy differences
• Quantum entanglement due to modulated Dynamical Casimir Effect
• Distributed Compression and Multiparty Squashed Entanglement
• The conditional entropy power inequality for Gaussian quantum states
• Squashed entanglement and approximate private states
• The conditional Entropy Power Inequality for bosonic quantum systems
• Entanglement production in the dynamical Casimir effect at parametric resonance
• Gaussian optimizers for entropic inequalities in quantum information
• Towards Spacetime Entanglement Entropy for Interacting Theories
• Squashed entanglement in infinite dimensions
• Entanglement entropy converges to classical entropy around periodic orbits
• Entropy of a subalgebra of observables and the geometric entanglement entropy
• Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous variable systems
• The conditional entropy power inequality for quantum additive noise channels
• Geometric inequalities from phase space translations
• Separability of Density Matrices and Conditional Information Transmission
• Relaxation Method For Calculating Quantum Entanglement
• New lower bounds to the output entropy of multi-mode quantum Gaussian channels
• Bosonic and fermionic Gaussian states from Kähler structures
• Entanglement of Formation and Conditional Information Transmission
• The Entropy Power Inequality with quantum conditioning
• A toy model for time evolving QFT on a lattice with controllable chaos
• Gaussian optimizers and other topics in quantum information
• Entanglement of Bell Mixtures of Two Qubits

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• The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems