Freeness Reined in by a Single Qubit
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911321903071232 |
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| author | Altland, Alexander Divi, Francisco Micklitz, Tobias Rezaei, Maedeh |
| author_facet | Altland, Alexander Divi, Francisco Micklitz, Tobias Rezaei, Maedeh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Freeness Reined in by a Single Qubit Altland, Alexander Divi, Francisco Micklitz, Tobias Rezaei, Maedeh Quantum Physics Disordered Systems and Neural Networks 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. |
| title | Freeness Reined in by a Single Qubit |
| topic | Quantum Physics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2512.13803 |