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

@inproceedings{Palma2021LinearGO, title={Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states}, author={Giacomo De Palma and Lucas Hackl}, year={2021} }

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… Expand

#### References

SHOWING 1-10 OF 76 REFERENCES

Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate

- Physics
- 2017

A bstractThe rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate hKS given by the sum of all positive Lyapunov exponents of the system. We… Expand

Entanglement production in bosonic systems: Linear and logarithmic growth

- Physics
- 2018

We study the time evolution of the entanglement entropy in bosonic systems with time-independent, or time-periodic, Hamiltonians. In the first part, we focus on quadratic Hamiltonians and Gaussian… Expand

Entanglement dynamics after quantum quenches in generic integrable systems

- Physics
- 2017

The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by… Expand

Entanglement and thermodynamics after a quantum quench in integrable systems

- Physics, Mathematics
- Proceedings of the National Academy of Sciences
- 2017

It is shown that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the steady state and its excitations, leads to a complete understanding of theEntanglement dynamics in the space–time scaling limit. Expand

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

- Physics, Mathematics
- 2021

We prove a generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum Gaussian systems. Such generalization determines the minimum values of linear combinations of the… Expand

Towards Spacetime Entanglement Entropy for Interacting Theories

- Physics
- 2020

Entanglement entropy of quantum fields in gravitational settings is a topic of growing importance. This entropy of entanglement is conventionally computed relative to Cauchy hypersurfaces where it is… Expand

Entanglement entropy converges to classical entropy around periodic orbits

- Physics
- 2015

We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic… Expand

Entanglement entropy of squeezed vacua on a lattice

- Physics
- 2015

We derive a formula for the entanglement entropy of squeezed states on a lattice in terms of the complex structure J. The analysis involves the identification of squeezed states with… Expand

The Conditional Entropy Power Inequality for Bosonic Quantum Systems

- Mathematics
- 2017

We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the… Expand

Quantum entanglement due to a modulated dynamical Casimir effect

- Physics
- 2014

We study the creation and entanglement of quasiparticle pairs due to a periodic variation of the mode frequencies of a homogeneous quantum system. Depending on the values of the parameters describing… Expand