Quantum information scrambling in the presence of weak and strong thermalization

Quantum information scrambling under the dynamics of a closed many-body system is of wide interest. The tripartite mutual information (TMI) can quantify the scrambling via its stable negative value under temporal evolution. Here, we study the quench dynamics of the TMI in a nonintegrable Ising model with different initial states in the regimes of strong and weak thermalization. Our numerical results show that the most efficient scrambling can occur when the inverse temperatures of initial states are near zero and in the regime of strong thermalization, and weak thermalization accompanies slow scrambling. We then present an experimental protocol for observing strong and weak thermalization in a one-dimensional array of superconducting qubits, based on which the relation between scrambling and the degree of thermalization revealed in this work can be directly verified by superconducting quantum simulators. The inevitable decoherence effects in real situations are also analyzed, paving the way for faithful quantum simulations on actual experimental platforms.