Digital Supplement for Enhancing Collective Entanglement Witnesses through Correlation with State Purity

This paper analyzes the adverse impact of white noise on collective quantum measurements and argues that such noise poses a significant obstacle for the otherwise straightforward deployment of collective measurements in quantum communications. The paper then suggests addressing this issue by correlating outcomes of these measurements with quantum state purity. To test the concept, a support vector machine is employed to boost the performance of several collective entanglement witnesses by incorporating state purity into the classification task of distinguishing entangled states from separable ones. Furthermore, the application of machine learning allows to optimize {specificity} of entanglement detection given a target value of sensitivity. A response operating characteristic curve is reconstructed based on this optimization and the area under curve calculated to assess the efficacy of the proposed model. {Finally, we test the presented approach on an experimental dataset of Werner states.