Probing Entanglement and Symmetries in Random States Using a Superconducting Quantum Processor

TL;DR

This paper experimentally investigates the entanglement and symmetries of random many-body quantum states generated by ergodic Floquet models on a superconducting quantum processor, confirming theoretical predictions about universal features.

Contribution

It demonstrates the experimental measurement of entanglement entropy, subsystem symmetries, and entanglement phases in random quantum states, bridging theory and experiment in quantum many-body physics.

Findings

Measured the Page curve of entanglement entropy.

Probed subsystem symmetries using entanglement asymmetry.

Revealed distinct entanglement phases through moments of partially transposed density matrices.

Abstract

Quantum many-body systems display an extraordinary degree of complexity, yet many of their features are universal: they depend not on microscopic details, but on a few fundamental physical aspects such as symmetries. A central challenge is to distill these universal characteristics from model-specific ones. Random quantum states sampled from a uniform distribution, the Haar measure, provide a powerful framework for capturing this typicality. Here, we experimentally study the entanglement and symmetries of random many-body quantum states generated by evolving simple product states under ergodic Floquet models. We find excellent agreement with the predictions from the Haar-random state ensemble. First, we measure the R\'enyi-2 entanglement entropy as a function of the subsystem size, observing the Page curve. Second, we probe the subsystem symmetries using entanglement asymmetry. Finally, we measure the moments of partially transposed reduced density matrices obtained by tracing out part of the system in the generated ensembles, thereby revealing distinct entanglement phases. Our results offer an experimental perspective on the typical entanglement and symmetries of many-body quantum systems.