2025/12/15 by Alexander Altland, Francisco Divi, Altland, Alexander +5
Computer Science · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum many-body systems
paper · doi:10.48550/arxiv.2512.13803
openalex publication_date 2025/12/15 · openalex created_date 2025/12/18 · openalex updated_date 2026/07/28
Free probability provides a framework for describing correlations between noncommuting observables in complex quantum systems whose Hilbert-space states follow maximum-entropy distributions. We examine the robustness of this framework under a minimal deviation from freeness: the coupling of a single ancilla qubit to a Haar-distributed quantum circuit of dimension D0≫1. We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order O(1). These modifications persist at long times, when the dynamics of the coupled system is already ergodic. We trace their origin to nonuniformly distributed stationary quantum states, which we characterize analytically and confirm numerically.