Protecting entanglement witnesses with randomized measurements

Abstract: Entanglement is one of the most prominent features of quantum mechanics and serves as an essential resource in quantum information science. Therefore, the certification of entanglement is crucial for quantum information processing tasks. While entanglement witnesses are the most frequently used method for entanglement certification in experiments, recent research shows that even tiny errors in measurements may significantly undermine the effectiveness of a witness. In this work, we propose a randomized-measurement-based method to solve this problem. Through this method, the errors in measurement results can be substantially suppressed, thereby restoring the certification capability of entanglement witnesses. Our method is not only applicable to general types of witnesses, including multi-party entanglement and high-dimensional entanglement witnesses, but also experimentally friendly in the sense that only slight modifications are needed to the original measurement settings.