Quantum-Limited Blind Source Separation of Classical Light

Using the framework of quantum multiparameter estimation, we study the problem of separating independent thermal optical sources mixed by an unknown passive linear transformation, which is known as blind source separation in signal processing. We propose a sensing-assisted method that iteratively estimates and suppresses optical correlations directly within the unit cells of a programmable interferometer. We show that collective quantum measurements exhibit a substantial advantage over conventional detection methods by constructing collective measurements that asymptotically achieve the Holevo Cram\'er--Rao bound in a unit cell of the interferometer for the respective sub-problem. By systematically arranging multiple such cells in a photonic mesh, our proposal implements an in situ Jacobi diagonalization of the input multimode correlation matrix. We contrast our method with a conventional approach where heterodyne detection is used to reconstruct the full covariance matrix and subsequently diagonalize it on a classical computer. A comparison with this heterodyne tomography approach shows that our sensing-based method is particularly advantageous in the weak-light regime.