Quantum correlations and entanglement are fundamental resources for quantum information and quantum communication processes. Developments in these fields normally assume stable resources, not susceptible of distortion. That is not always the case, Heisenberg interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e. g. quantum computation or quantum cryptography). The presence of parasite magnetic fields modifies the expected properties and behavior for which the pair was intended. Quantum measurement and control help to discriminate the original state in order to correct it or reconstruct it using some procedures which do not alter their quantum nature. Different kinds of quantum entangled pairs driven by a Heisenberg Hamiltonian with an additional inhomogeneous magnetic field become distorted. They can be reconstructed by adding an external magnetic field with fidelity close to one. In addition, each state can be efficiently discriminated. Combining both processes, first reconstruction without discrimination and after discrimination with adequate non-local measurements, it is possible to (a) improve the discrimination, and (b) reprepare faithfully the original state. The complete process gives fidelities better than 0.9. Some results about a class of equivalence for the required measurements are found, allowing to select the experimentally most adequate.
Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations
