Dynamical Phase Transitions Induced by Conditional Mutual Information's Propagation Beyond the Lightcone

Understanding the dynamics of noisy random circuits holds significant theoretical importance and practical relevance. In our study of an N-qubit system subjected to noisy random unitary gates with an error rate p, we observe and analyze the dynamical phase transition of entanglement at the thermodynamic limit where N → ∞ and p → 0. The main discovery of our work is that the phase transition is spurred by the spreading of conditional mutual information (CMI). Specifically, we remark that the total correlation can be dissected into that of subparts and the CMI. Notably, we uncover the anomalous behavior of the CMI: while the spread of general correlations is bounded by the causal lightcone, CMI exhibits superlinear propagation, enabling it to surpass the lightcone. Validating this notion through numerical simulations, our work reveals that the superluminal spreading of CMI induces the sharp transition of entanglement dynamics in noisy circuits.