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This paper analyzes the adverse impact of white noise on collective quantummeasurements and argues that such noise poses a significant obstacle to theotherwise straightforward deployment of collective measurements in quantumcommunications. The paper then suggests addressing this issue by correlatingthe outcomes of these measurements with quantum state purity. To test theconcept, a support vector machine is employed to boost the performance ofseveral collective entanglement witnesses by incorporating state purity intothe classification task of distinguishing entangled states from separable ones.Furthermore, the application of machine learning allows to optimize selectivityof entanglement detection given a target value of sensitivity. A responseoperating characteristic curve is reconstructed based on this optimization andthe area under curve calculated to assess the efficacy of the proposed model.

Enhancing collective entanglement witnesses through correlation with state purity