Related papers: Quantifying operator spreading and chaos in Krylov…
Operator scrambling denotes the evolution of a simple operator into a complicated one (in the Heisenberg picture), which characterizes quantum chaos in many-body systems. More specifically, a simple operator evolves into a linear…
We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This…
Operator growth, or operator spreading, describes the process where a "simple" operator acquires increasing complexity under the Heisenberg time evolution of a chaotic dynamics, therefore has been a key concept in the study of quantum chaos…
Recently, the concept of spread complexity, Krylov complexity for states, has been introduced as a measure of the complexity and chaoticity of quantum systems. In this paper, we study the spread complexity of the thermofield double state…
Operator scrambling is a crucial ingredient of quantum chaos. Specifically, in the quantum chaotic system, a simple operator can become increasingly complicated under unitary time evolution. This can be diagnosed by various measures such as…
Chaotic systems are highly sensitive to a small perturbation, and are ubiquitous throughout biological sciences, physical sciences and even social sciences. Taking this as the underlying principle, we construct an operational notion for…
Interaction in quantum systems can spread initially localized quantum information into the many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is the key to resolving various conundrums in…
The non-integrability of quantum systems, often associated with chaotic behavior, is a concept typically applied to cases with a high-dimensional Hilbert space Among different indicators signaling this behavior, the study of the long-time…
Recently, the propagation of information through quantum many-body systems, developed to study quantum chaos, have found many application from black holes to disordered spin systems. Among other quantitative tools, Krylov complexity has…
We investigate the quantitative relationship between operator spreading and classical information propagation in quantum systems. Focusing on a bi-partite quantum channel, we derive new upper and lower bounds on the Holevo capacity, a…
The dynamical spreading of quantum information through a many-body system, typically called scrambling, is a complex process that has proven to be essential to describe many properties of out-of-equilibrium quantum systems. Scrambling can,…
The spreading of entanglement in out-of-equilibrium quantum systems is currently at the centre of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we…
In this article we study a set of integrable quantum cellular automata,the quantum hardcore gases (QHCG), with an arbitrary local Hilbert space dimension, and discuss the matrix product ansatz based approach for solving the dynamics of…
Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the…
We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under application of…
Out-of-time-order correlators (OTOCs) have been proposed as a probe of chaos in quantum mechanics, on the basis of their short-time exponential growth found in some particular set-ups. However, it has been seen that this behavior is not…
Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout the entire system. This concept underlies the dynamics of thermalization in closed quantum systems, and…
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…
This work develops tools to understand how quantum information spreads, scrambles, and is reshaped by measurements in many-body systems. First, I study scrambling and pseudorandomness in the Brownian Sachdev-Ye-Kitaev (SYK) model,…
We introduce a quantity called the free mutual information (FMI), adapted from concepts in free probability theory, as a new physical measure of quantum chaos. This quantity captures the spreading of a time-evolved operator in the space of…