Maximum likelihood blind separation of two quantum states (qubits) with cylindrical-symmetry Heisenberg spin coupling

Blind source separation (BSS) and quantum information processing (QIP) are two recent and rapidly evolving fields. No connection has ever been made between them to our knowledge, except in our initial paper, However, future practical QIP systems will probably involve "observed mixtures", in the BSS sense, of quantum states (qubits), e.g. associated to coupled spins. We here investigate how individual qubits may be retrieved from cylindrical-symmetry Heisenberg-coupled versions of them, and we show the relationship between this problem and classical BSS. We thus introduce a new nonlinear mixture model for qubits, motivated by actual quantum physical devices. We analyze the invertibility and ambiguities of this model. We propose practical data processing methods for (i) estimating the mixing parameter with a maximum likelihood approach and (ii) performing inversion to retrieve the sources. This yields a major extension as compared to our previous paper, not only in terms of considered spin coupling model, but also because we here introduce a much more powerful mixture estimation procedure.