Exact and Approximate Quantum Independent Component Analysis for Qubit Uncoupling

摘要

As a tool for solving the Blind Quantum Source Separation problem introduced in our previous papers, we here propose the concept of Quantum Independent Component Analysis (QICA). Starting from quantum bits (qubits) with cylindrical-symmetry Heisenberg coupling, quantum-to-classical conversion yields an original nonlinear mixing model, which leads us to develop QICA methods dedicated to this model. Our first method consists in minimizing the mutual information of the outputs of our nonlinear separating system. It is attractive because it yields an exact solution, without any spurious points thanks to the (Q)ICA separability of the considered model. The second proposed method is a simpler approximation of the first one. It is based on a truncated expansion of differential entropy (or negentropy), derived from the Edgeworth expansion of probability density functions.