Statistical Methods for Quantum State Verification and Fidelity Estimation

TL;DR

This paper reviews recent statistical methods for efficiently verifying and estimating the fidelity of quantum states, emphasizing hypothesis testing and strategies for entangled states, quantum channels, and entanglement verification.

Contribution

It provides a comprehensive overview of recent advances in statistical quantum state verification, including new strategies and extensions for complex quantum systems.

Findings

Various hypothesis testing approaches for quantum state verification

Strategies for entangled state verification with local measurements

Extensions to quantum channel certification and entanglement verification

Abstract

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 we present a review of the recent progress in this field. We first explain how the verification and fidelity estimation of a quantum state can be discussed in the language of hypothesis testing. Then, we explain in detail various strategies for the verification of entangled states with local measurements or measurements assisted by local operations and classical communication. Finally, we discuss several extensions of the problem, such as the certification of quantum channels and the verification of entanglement.