A new study introduces a theoretical framework based on the Haar-averaged sum of total correlations (aSTC) to characterize integrability and chaos in quantum systems. This method, which also considers dynamically generated genuine multipartite entanglement, offers a robust probe for quantum information scrambling. The researchers have shown that both the long-time average and, crucially, the temporal fluctuations of the aSTC provide a faithful and system-size-independent signature for distinguishing between integrable and chaotic dynamics, similar to the out-of-time-ordered correlator (OTOC), a conventional measure of scrambling.

The team applied this framework to the long-range quantum XYZ spin model, which includes the nearest-neighbor transverse XY model as its integrable limit. In open quantum systems, where they interact with a thermal reservoir, it was observed that fluctuations of both aSTC and OTOC distinguish integrability only at intermediate times if the system-bath coupling is Markovian. However, in the non-Markovian regime, information backflow restores the scrambling dynamics, allowing the aSTC to retain its distinguishing power even at long times.

A notable finding is that, under certain types of noise (Markovian amplitude damping and non-Markovian dephasing noise), the temporal fluctuations of the aSTC can discriminate between integrability and non-integrability in the weak Markovian regime, even when the OTOC fails to do so. This highlights the robustness and utility of aSTC as a tool for exploring the fundamental properties of quantum dynamics, especially in noisy and complex environments.