Verification of entangled states under noisy measurements

TL;DR

This paper systematically analyzes quantum state verification under measurement noise, providing conditions for unique state identification, proposing a verification algorithm, and demonstrating its effectiveness through analytical and numerical results.

Contribution

It introduces a necessary and sufficient condition for verifying entangled states with noisy measurements and proposes a symmetric hypothesis testing verification algorithm.

Findings

Verification efficiency decreases quadratically with noise level.

The proposed method is applicable to real experimental setups.

Noise impacts the sample complexity in a predictable manner.

Abstract

Entanglement plays an indispensable role in numerous quantum information and quantum computation tasks, underscoring the need for efficiently verifying entangled states. In recent years, quantum state verification has received increasing attention, yet the challenge of addressing noise effects in implementing this approach remains unsolved. In this work, we provide a systematic assessment of the performance of quantum state verification protocols in the presence of measurement noise. Based on the analysis, a necessary and sufficient condition is provided to uniquely identify the target state under noisy measurements. Moreover, we propose a symmetric hypothesis testing verification algorithm with noisy measurements. Subsequently, using a noisy nonadaptive verification strategy of GHZ and stabilizer states, the noise effects on the verification efficiency are illustrated. From both analytical and numerical perspectives, we demonstrate that the noisy verification protocol exhibits a negative quadratic relationship between the sample complexity and the infidelity. Our method can be easily applied to real experimental settings, thereby demonstrating its promising prospects.