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 …

A bstract The emergence of the bulk Hilbert space is a mysterious concept in holography. In
[1], the SYK model was solved in the double scaling limit by summing chord diagrams. Here …

The double-scaled limit of the Sachdev-Ye-Kitaev (SYK) model takes the number of fermions
and their interaction number to infinity in a coordinated way. In this limit, two entangled …

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 …

This tutorial article introduces the physics of quantum information scrambling in quantum
many-body systems. The goals are to understand how to precisely quantify the spreading of …