We review the mathematical speed limits on quantum information processing in many-body
systems. After the proof of the Lieb–Robinson Theorem in 1972, the past two decades have …

We give a pedagogical review of how concepts from quantum information theory build up
the gravitational side of the anti-de Sitter/conformal field theory correspondence. The review …

We develop a geometric approach to operator growth and Krylov complexity in many-body
quantum systems governed by symmetries. We start by showing a direct link between a …

A bstract We study the operator growth in open quantum systems with dephasing dissipation
terms, extending the Krylov complexity formalism of [1]. Our results are based on the study of …

A bstract Krylov complexity measures the spread of the wavefunction in the Krylov basis,
which is constructed using the Hamiltonian and an initial state. We investigate the evolution …

We present a hypothesis for the universal properties of operators evolving under
Hamiltonian dynamics in many-body systems. The hypothesis states that successive …

A bstract Heisenberg time evolution under a chaotic many-body Hamiltonian H transforms
an initially simple operator into an increasingly complex one, as it spreads over Hilbert …

Entanglement, chaos, and complexity are as important for de Sitter space as for AdS and for
black holes. There are similarities and great differences between AdS and dS in how these …

Krylov complexity is a measure of operator complexity that exhibits universal behavior and
bounds a large class of other measures. In this paper, we generalize Krylov complexity from …

A bstract We use Krylov complexity to study operator growth in the q-body dissipative
Sachdev-Ye-Kitaev (SYK) model, where the dissipation is modeled by linear and random p …