For a wide range of applications, a fast, non-destructive, remote, and sensitive identification of samples with predefined characteristics is preferred instead of their full characterization. In this work, we report on the experimental implementation of a nonlocal quantum measurement scheme, which allows for differentiation among samples out of a predefined set of transparent and birefringent objects in a distant optical channel. The measurement is enabled by application of polarization-entangled photon pairs and is based on remote state preparation. On an example set of more than 80 objects characterized by different Mueller matrices, we show that only two coincidence measurements are already sufficient for successful discrimination. The number of measurements needed for sample differentiation is significantly decreased compared to a comprehensive polarimetric analysis. Our results demonstrate the potential of this polarization detection method for polarimetric applications in biomedical diagnostics, remote sensing, and other classification/detection tasks.