Jones matrix reconstruction with undetected photons

We propose a theoretical polarization tomography scheme within the quantum imaging with undetected photons (QIUP) framework that extracts the Jones matrix elements, describing the sample's polarization response from interference visibilities and phase shifts. By exploiting inherent constraints among the Jones matrix elements based on the assumptions of fully polarized pure states and linear, non-depolarizing components, the method reduces the number of unknowns required for reliable reconstruction. The same interference-based protocol is also demonstrated for a fully generalized Jones matrix, extending the approach to a broader class of polarization responses. This scheme is well suited for polarization-resolved QIUP implementations with minimal measurement requirements and enables non-invasive characterization of complex samples at different probing and detection wavelengths.