  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.
