Density matrix reconstruction using a Hong–Ou–Mandel quantum interferometer

We provide a comprehensive analysis of the reconstruction of the density matrix for entangled photon pairs, utilizing polarization measurements within a Hong–Ou–Mandel (HOM) interference framework. The purpose of this study is to develop a new efficient approach for quantum state characterization, leveraging quantum interference to reduce wave dispersion and utilizing the maximum likelihood method for density matrix reconstruction. The model involves projecting the entangled photons onto a set of sixteen unique polarization states, enabling the observation of detailed quantum interference patterns. We use these patterns to reconstruct the density matrix, revealing the system’s quantum state and degree of entanglement. Our findings demonstrate the effectiveness of this method in accurately characterizing the quantum state of light, while leveraging quantum interference to reduce wave dispersion and improve signal quality and resolution. Our study underscores the effectiveness of this method in accurately characterizing the quantum state of light and highlights the essential role of precise density matrix reconstruction in a Hong–Ou–Mandel interferometer without the use of polarizers. The methodology and results presented lay a strong foundation for further research, with implications for improving measurement accuracy and exploring more complex quantum systems in various quantum information applications.