This research 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. Our findings 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.

Institute of Physics of the Academy of Sciences of the Czech Republic Joint Laboratory of Optics of Palacký University and Institute of Physics AS CR 17 listopadu 50a 772 07 Olomouc Czech Republic

Institute of Theoretical Physics University of Wroclaw Plac Maxa Borna 9 50 204 Wroclaw Poland

Joint Laboratory of Optics of Palacký University Institute of Physics AS CR Faculty of Science Palacký University in Olomouc 17 listopadu 12 771 46 Olomouc Czech Republic

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