Statistical Methods for Quantum State Verification and Fidelity Estimation - Yu, Xiao‐Dong; Shang, Jiangwei; Gühne, Otfried (Advanced quantum technologies (Online), 2022)
The efficient and reliable certification of quantum states is essential for various quantum information processing tasks as well as for the general progress on the implementation of quantum technologies. In the last few years several methods have been introduced which use advanced statistical methods to certify quantum states in a resource‐efficient manner. In this article, a review of the recent progress in this field is presented. How the verification and fidelity estimation of a quantum state can be discussed in the language of hypothesis testing is explained first. Then, various strategies for the verification of entangled states with local measurements or measurements assisted by local operations and classical communication are explained in detail. Finally, several extensions of the problem, such as the certification of quantum channels and the verification of entanglement are discussed. How can one verify that a certain quantum state has been prepared in a quantum device? This question is essential for various tasks in quantum information processing. This article presents a pedagogical review on this topic. Starting from the theory of hypothesis testing, the current protocols for quantum state verification and fidelity estimation are explained.