despite being initially farther from equilibrium， relaxes faster than a closer counterpart. Detecting such a quantum Mpemba effect typically requires full knowledge of the quantum state during its time evolution， as long as the system equilibrates to a known unique steady-state， it is possible to fully detect the occurrence of quantum Mpemba effect just by measuring the observable for known state preparations. Our approach thus significantly reduces experimental complexity and offers a practical route for observing the quantum Mpemba effect in complex and extended multi-qubit setups. ， which is an experimentally challenging task since state tomography becomes exponentially difficult as system size increases. This poses a significant obstacle in studying Mpemba effect in complex many-body systems. In this work。
we demonstrate that this limitation can be overcome by identifying suitable observables that signal rapid relaxation. Moreover， The Mpemba effect refers to the anomalous relaxation of a quantum state that，。