The Scrooge ensemble in many-body quantum systems

• URL: http://arxiv.org/abs/2511.17172v1
• Date: Fri, 21 Nov 2025 11:46:44 GMT
• Title: The Scrooge ensemble in many-body quantum systems
• Authors: Max McGinley, Thomas Schuster,
• Abstract summary: We prove several key results on the properties and complexity of Scrooge-random states in macroscopic quantum systems.<n>A key theme of our results is a separation between universal random fluctuations in non-local properties and exponential concentration of all local properties.
• Score: 0.003036798645685547
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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