A blind quantum source separation method based on mutual information for retrieving two qubits with cylindrical-symmetry heisenberg coupling

This paper concerns the blind quantum source separation (BQSS) field, that we introduced previously. More specifically, we investigate how to retrieve individual quantum states, after they were coupled according to the cylindrical-symmetry Heisenberg model and converted into classical data by means of measurements. The statistical method that we propose to perform this separation consists in minimizing the cost function defined as the mutual information of the outputs of our separating system, which is tailored to the considered nonlinear coupling model. This method is especially attractive because its cost function has no global spurious points, i.e. it has a single global minimum value, obtained when source separation is achieved (thanks to the ICA separability of the considered nonlinear global model). In this paper, we address all major aspects of this approach, including the definition of the considered separation criterion and of an associated optimization algorithm, and the derivations of the expressions of all the quantities involved in this algorithm.