Jones Matrix Reconstruction with Undetected Photons

Abstract: We present a theoretical polarization tomography scheme within the QIUP framework that directly extracts key sample parameters from measured interference visibilities and phase shifts. This approach establishes constant bindings for transmission amplitudes and coherence terms, thereby reducing the number of unknowns required to reconstruct the sample's Jones matrix. Our method is resource-efficient and well-suited for quantum imaging where probing and detection occur at different wavelengths, enabling robust, non-invasive characterization of complex samples.