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arXiv · 2511.17172

The Scrooge ensemble in many-body quantum systems

Max McGinley·Thomas Schuster
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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.

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Max McGinley, Thomas Schuster. 2025-11-21. The Scrooge ensemble in many-body quantum systems. https://arxiv.org/abs/2511.17172

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