The Scrooge ensemble in many-body quantum systems
AI Breakdown
Get a structured breakdown of this paper — what it's about, the core idea, and key takeaways for the field.
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.