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Developing quantum technologies requires the control and understanding of thenon-equilibrium dynamics of quantum information in many-body systems. Localinformation propagates in the system by creating complex correlations known asinformation scrambling, as this process prevents extracting the informationfrom local measurements. In this work, we develop a model adapted fromsolid-state NMR methods, to quantify the information scrambling. The scramblingis measured via time-reversal Loschmidt echoes (LE) and Multiple QuantumCoherences experiments that intrinsically contain imperfections. Consideringthese imperfections, we derive expressions for out-of-time-order correlators(OTOCs) to quantify the observable information scrambling based on measuringthe number of active spins where the information was spread. Based on the OTOCexpressions, decoherence effects arise naturally by the effects of thenonreverted terms in the LE experiment. Decoherence induces localization of themeasurable degree of information scrambling. These effects define alocalization cluster size for the observable number of active spins thatdetermines a dynamical equilibrium. We contrast the model's predictions withquantum simulations performed with solid-state NMR experiments, that measurethe information scrambling with time-reversal echoes with controlledimperfections. An excellent quantitative agreement is found with the dynamicsof quantum information scrambling and its localization effects determined fromthe experimental data. The presented model and derived OTOCs set tools forquantifying the quantum information dynamics of large quantum systems (morethan $10^{4}$ spins) consistent with experimental implementations thatintrinsically contain imperfections.

Dynamics of quantum information scrambling under decoherence effects measured via active spins clusters