A new general quantum state verification protocol by the classical shadow method

Verifying whether a quantum device produces a specific state is a fundamental task in many applications of modern quantum technologies. In the conventional framework of quantum state verification, designing an optimal or efficient protocol for each type of state often requires intricate customization. Recently, Hsin-Yuan Huang et al. introduced a novel approach called the shadow overlap protocol in arXiv:2404.07281v1, which leverages classical shadows to efficiently verify multiple types of states simultaneously. In this paper, we propose a new verification protocol that integrates key ideas from both the conventional framework and the shadow overlap protocol. To achieve this, we first reformulate the shadow overlap protocol using the language of hypothesis testing, which also underpins the conventional framework, and then analyze the similarities and differences between them. Our approach enhances the capabilities of the shadow overlap protocol while addressing some of its limitations, leading to improved sample complexity and a more natural treatment of states with specific structures. Finally, we demonstrate the effectiveness of our protocol by applying it to GHZ states and stabilizer states.