The Scrooge ensemble in many-body quantum systems

TL;DR

This paper investigates the properties and complexity of Scrooge ensemble states in many-body quantum systems, revealing their unique fluctuation and concentration behaviors with implications for quantum benchmarking and complexity.

Contribution

It provides rigorous results and a calculus for analyzing Scrooge-random states, highlighting their distinct non-local and local property behaviors in macroscopic quantum systems.

Findings

Separation between universal non-local fluctuations and local concentration.

A general calculus for evaluating moments of Scrooge states.

Implications for quantum device benchmarking and complexity growth.

Abstract

In many physical settings, the statistical properties of quantum states are thought to be described by the Scrooge ensemble, a more structured generalization of the Haar ensemble. In this work, we prove several key results on the properties and complexity of Scrooge-random states in macroscopic quantum systems, and provide a general-purpose calculus for evaluating their moments. A key theme of our results is a separation between universal random fluctuations in non-local properties and exponential concentration of all local properties. Implications for device benchmarking, sampling advantages beyond random circuits, quantum complexity growth, and the physical origin of Scrooge-random states are discussed.