Freeness Reined in by a Single Qubit

• URL: http://arxiv.org/abs/2512.13803v1
• Date: Mon, 15 Dec 2025 19:00:09 GMT
• Title: Freeness Reined in by a Single Qubit
• Authors: Alexander Altland, Francisco Divi, Tobias Micklitz, Maedeh Rezaei,
• Abstract summary: We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order $O(1)$.<n>We trace their origin to non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically.
• Score: 36.94429692322632
• License: http://creativecommons.org/licenses/by/4.0/
• 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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