Related papers: Operator Growth and Symmetry-Resolved Coefficient …
We study non-equilibrium dynamics induced by a sudden quench of strongly correlated Hamiltonians with all-to-all interactions. By relying on a Sachdev-Ye-Kitaev (SYK) based quench protocol, we show that the time evolution of simple…
Covert and secret quantum key distribution aims at generating information-theoretically secret bits between distant legitimate parties in a manner that remains provably undetectable by an adversary. We propose a framework in which to…
Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be…
The notion of operator growth in quantum systems furnishes a bridge between transport and the generation of entanglement between different parts of the system under quantum dynamics. We define a measure of operator growth in terms of…
We introduce quantum circuits in two and three spatial dimensions which are classically simulable, despite producing a high degree of operator entanglement. We provide a partial characterization of these "automaton" quantum circuits, and…
In closed generic many-body systems, unitary evolution disperses local quantum information into highly non-local objects, resulting in thermalization. Such a process is called information scrambling, whose swiftness is quantified by the…
Quantum operator scrambling describes the spreading of local operators into the whole system in the picture of Heisenberg evolution, which is often quantified by the operator size growth. Here we propose a measure of quantum operator…
We study the operator growth in open quantum systems with dephasing dissipation terms, extending the Krylov complexity formalism of Phys. Rev. X 9, 041017. Our results are based on the study of the dissipative $q$-body Sachdev-Ye-Kitaev…
Scrambling, a process in which quantum information spreads over a complex quantum system becoming inaccessible to simple probes, happens in generic chaotic quantum many-body systems, ranging from spin chains, to metals, even to black holes.…
The breakdown of Lieb-Robinson bounds in local, non-Hermitian quantum systems opens up the possibility for a rich landscape of quantum many-body phenomenology. We elucidate this by studying information scrambling and quantum chaos in…
We show that there are well separated families of quantum expanders with asymptotically the maximal cardinality allowed by a known upper bound. This has applications to the "growth" of certain operator spaces: It implies asymptotically…
Operator scrambling, which governs the spread of quantum information in many-body systems, is a central concept in both condensed matter and high-energy physics. Accurately capturing the emergent properties of these systems remains a…
Understanding the spreading of the operator space entanglement entropy ($OSEE$) is key in order to explore out-of-equilibrium quantum many-body systems. Here we argue that for integrable models the dynamics of the $OSEE$ is related to the…
We investigate the operator growth dynamics of the transverse field Ising spin chain in one dimension as varying the strength of the longitudinal field. An operator in the Heisenberg picture spreads in the extended Hilbert space. Recently,…
When a quantum system initialized in a product state is subjected to either coherent or incoherent dynamics, the entropy of any of its connected partitions generically increases as a function of time, signalling the inevitable spreading of…
Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and…
In this work, we derive an exact hydrodynamical description for the coupled, charge and operator dynamics, in a quantum many-body system with U(1) symmetry. Using an emergent symmetry in the complex Brownian SYK model with charge…
The time evolution of local operators in quantum compass models is characterized by simplicity as it can be represented as expanding and contracting strings of operators. Here we present an analytical solution to the problem of growth of a…
We give a detailed theory for the leading coarse-grained dynamics of entanglement entropy of states and of operators in generic short-range interacting quantum many-body systems. This includes operators spreading under Heisenberg time…
Some quantum algorithms have "quantum speedups": improved time complexity as compared with the best-known classical algorithms for solving the same tasks. Can we understand what fuels these speedups from an entropic perspective? Information…