Abstract: The holographic entanglement entropy is a very useful tool in studying the information-theoretic aspects of AdS/CFT, and its efficacy is manifested in the recent black hole page curve calculation. On the other hand, the one-shot entropies, such as the smooth min/max-entropies, are less discussed in AdS/CFT. They are however more fundamental entropy measures from the quantum information perspective and should also play pivotal roles in holography. We combine the technical methods from both quantum information and quantum gravity to put this idea on firm grounds. In particular, we study the quantum minimal surface (QMS) prescription that was recently revised by Akers and Penington to highlight the significance of one-shot entropies in characterising the QMS phase transition. Motivated by the asymptotic equipartition property (AEP), we derive the refined QMS prescription for fixed-area states via a novel AEP replica trick that involves the opposite limit of infinite replicas. Our derivation leverages several tools from the one-shot information theory that could potentially be useful in other applications.