Blind Separation of Quantum States: Estimating Two Qubits from an Isotropic Heisenberg Spin Coupling Model

Abstract

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. 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 Heisenberg-coupled versions of them, and we show the relationship between this problem and classical BSS. We thus introduce new nonlinear mixture models for qubits, motivated by actual quantum physical devices. We analyze the invertibility and ambiguities of these models. We propose practical data processing methods for performing inversions.