Blind quantum source separation: Quantum-processing qubit uncoupling systems based on disentanglement

Abstract

Blind Quantum Source Separation (BQSS) deals with multi-qubit states, called “mixed states”, obtained by applying an unknown “mixing function” (which typically corresponds to undesired coupling, e.g. between qubits implemented as close electron spins 1/2) to unknown multi-qubit “source states”, which are product states (and pure in the simplest case, considered in this paper). Some other properties are also possibly requested from these source states and/or mixing function. Using mixed states, BQSS systems aim at restoring (the information contained in) source states, during the second phase of their operation (“inversion phase”). To this end, they estimate the unmixing function (inverse of mixing function), during the first phase of their operation (“adaptation phase”). Most previously reported BQSS systems first convert mixed states into classical-form data, that they then process with classical means. Besides, they estimate the unmixing function by using statistical methods related to classical Independent Component Analysis. On the contrary, the new BQSS systems proposed here use only quantum-form data and quantum processing in the inversion phase, and they use classical-form data during the adaptation phase only. Moreover, their unmixing function estimation methods are essentially based on using unentangled source states during that phase. They mainly consist of disentangling the output quantum state of the separating system (for a few source states). Afterwards, they can also restore entangled source states. They yield major improvements over previous systems, concerning restored source parameters, associated indeterminacies and approximations, number of source states required for adaptation, numbers of source state preparations in adaptation and inversion phases. Numerical tests confirm that they accurately restore quantum source states.