ICA-based and second-order separability of nonlinear models involving reference signals: General properties and application to quantum bits

Relatively few results have been reported about the separability of given classes of nonlinear mixtures by means of statistical criteria such as ICA. We here first prove the ICA separability of a wide class of nonlinear global (i.e. mixing+separating) models involving “reference signals”, i.e. unmixed signals. We also show the second-order separability of sub-classes of the above class of models. This work therefore concerns nonlinear extensions of (linear) adaptive noise cancellation. We illustrate the usefulness of our general results by applying them to a quantum information processing problem, which involves a model of Heisenberg-coupled quantum states (i.e. qubits). This paper opens the way to practical ICA-based and second-order blind source separation (BSS) methods for nonlinear mixtures encountered in various applications. These BSS methods are also outlined in this paper.