Dynamics of steered quantum coherence and magic resource under sudden quench

We explore the dynamics of \(l_1\)-norm of steered quantum coherence (SQC), steered quantum relative entropy (SQRE), and magic resource quantifier (MRQ) in the one-dimensional XY spin chain in the presence of time-dependent transverse magnetic field. We find that the system’s response is highly sensitive to the initial state and magnetic field strength. We show the dynamics of SQC, SQRE, and MRQ revealing the critical point associated with equilibrium quantum phase transition (QPT) of the system. All quantities show maximum at QPT when the initial state is prepared in the ferromagnetic phase. Conversely, they undergo abrupt changes at quantum critical point if the initial state of the system is paramagnetic. Moreover, our results confirm that when quench is done to the quantum critical point, the first suppression (revival) time scales linearly with the system size, and remarkably, its scaling ratio remains consistent for all quenches, irrespective of the initial phase of the system. These results highlight the interplay between the quantum information resources and dynamics of quantum systems away from the equilibrium. Such insights could be vital for quantum information processing and understanding non-equilibrium phenomena in quantum many-body systems.