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arXiv · 2512.13803

Freeness Reined in by a Single Qubit

Alexander Altland·Francisco Divi·Tobias Micklitz·Maedeh Rezaei
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Abstract

Free probability provides a framework for describing correlations between non-commuting 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 $D0 \gg 1$. 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 non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically.

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Alexander Altland, Francisco Divi, Tobias Micklitz, Maedeh Rezaei. 2025-12-15. Freeness Reined in by a Single Qubit. https://arxiv.org/abs/2512.13803

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