Abstract
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 quantum information and how causality emerges in complex quantum systems. We introduce a general framework to study the dynamics of quantum information, including detection and decoding. We show that the dynamics of quantum information is closely related to operator dynamics in the Heisenberg picture, and, under certain circumstances, can be precisely quantified by the so-called out-of-time-ordered correlator (OTOC). The general behavior of the OTOC is discussed based on several toy models, including the Sachdev-Ye-Kitaev model, random circuit models, and Brownian models, in which the OTOC is analytically tractable. We introduce numerical methods, including exact diagonalization and tensor network methods, to calculate the OTOC for generic quantum many-body systems. We also survey current experimental schemes for measuring the OTOC in various quantum simulators.
- Received 14 February 2022
- Revised 9 May 2023
DOI:https://doi.org/10.1103/PRXQuantum.5.010201
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Alice tries to send a message to Bob through a chain of interacting qubits. However, as the message travels, it typically becomes delocalized. Consequently, Bob cannot read the message from a single qubit, which shortly appears in thermal equilibrium due to entanglement generation, regardless of what Alice initially sent. While the initial information is never lost, as quantum dynamics is reversible, it spreads to the nonlocal complex structure of the quantum state masked by the apparent simplicity of thermal equilibrium. This phenomenon is called quantum scrambling, which raises two key questions. First, how is Alice’s message distributed in the complex quantum state over time? Second, how can Bob recover the message?
Centered around the two key questions, this tutorial delves into scrambling dynamics in quantum many-body systems. We show that scrambling dynamics is characterized by nonlocal correlation in the quantum state, and Bob needs more than half of the qubits to recover the message in the late time. Scrambling dynamics can be observed in certain cases through a special local correlation function, called the out-of-time-ordered correlation function. We further discuss how out-of-time-ordered correlation, owing to its simplicity, can be calculated in certain toy models, numerically simulated in large systems, and measured experimentally. These results provide intuition about scrambling dynamics in general systems.
Looking forward, understanding scrambling dynamics is crucial to leveraging the interaction among quantum particles for protecting and coherently processing quantum information. Moreover, scrambling dynamics, closely related to the buildup of complexity in the quantum state, represent the starting point in characterizing long-time quantum dynamics beyond thermalization.
