Paper
Freeness Reined in by a Single Qubit
Authors
Alexander Altland, Francisco Divi, Tobias Micklitz, Maedeh Rezaei
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 . We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order . 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.