Dynamics of local quantum information in random unitary circuits

This paper investigates the fine-grained spatiotemporal anatomy of quantum information flow in many-body systems. Standard diagnostics like bipartite entanglement entropy are coarse-grained, effectively washing out the scale-by-scale structure of how information reorganizes during thermalization. To address this, the authors utilize the 'information lattice'—a two-dimensional framework where local information is resolved by both spatial location and length scale. By applying this to random unitary circuits (Haar-random and Clifford), the authors map the dynamics of local information onto an exact classical stochastic process, allowing them to track how information moves from smaller to larger length scales over time.

The study establishes that local information dynamics in chaotic systems are universal. For both Haar-random and Clifford circuits, the authors find that the average length scale at which information resides grows ballistically (proportional to time t), with a characteristic velocity 2vE. Crucially, the distribution of this information follows a Tracy-Widom form, and the fluctuations in the information length scale broaden as t^1/3. This scaling behavior suggests a deep connection between the microscopic dynamics of information flow and the Kardar-Parisi-Zhang (KPZ) universality class, which typically governs growing interfaces in classical statistical mechanics.

By resolving information flow at specific length scales, this work bridges the gap between exact microscopic theories of quantum dynamics and emergent hydrodynamic descriptions. It provides a more nuanced understanding of scrambling than traditional entanglement measures, offering a potential diagnostic tool for characterizing quantum states and phases. The framework also provides a concrete path for analyzing information dynamics in more complex settings, such as systems with conservation laws or measurement-induced phase transitions.

Information Lattice

A two-dimensional representation of a quantum state where each point (n, l) quantifies the information contained specifically at length scale l centered at position n.

Local Information

The quantum conditional mutual information that isolates the information content at a specific length scale, excluding contributions from smaller constituent subsystems.

Bigram

A classical object representing the extent of a stabilizer generator or minimal cut, which maps directly to a unit of local information on the information lattice.

Clipped Gauge

A specific choice of stabilizer generators for a Clifford state that makes the entanglement structure and bigram configuration transparent.

Entanglement Velocity (vE)

The speed at which entanglement entropy grows in a system, characterizing the rate of information scrambling.

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