Ricostruzione di stati multiqubit senza l’ausilio di tutti i valori dei correlatori

In recent years, there have been notable advancements in building and controlling large scale quantum systems with a variety of physical systems, as more interest and effort have been put into the research of quantum information processing. Even though it has proven realistic to build systems with a large number of qubits, it is still unclear how to assess these many-body states and characterize them completely. It is necessary indeed, in order to reconstruct the density matrix of the quantum state, to undertake numerous repetitions of measurement with multiple sets of basis. As a result, reconstructing the quantum state of a many-body system with a full quantum tomography requires the estimation of a number of parameters that grows exponentially with system size, leading to an unacceptable time complexity. For this reason, quantum tomography is one of the major challenges of large-scale quantum information research and numerous techniques have been studied and developed in order to overcome this problem. Indeed, situations in which it is possible to exploit parallelism in the measurement process or in which only a subset of the total number of parameters necessary to determine the state is needed can occur. In this work, we specifically focus on pure states and the minimum number of correlators required to reconstruct them. Our numerical analysis concerns strictly states with a size between three and seven qubits due to computational limits. Through numerical simulations we reconstruct a target pure state by taking into account only a fraction of the total number of correlators that characterize it, by trying different combinations and by making a parallelism with already existing protocols. We numerically demonstrate that it is still possible to determine the target pure state only by imposing a small portion of parameters in the reconstruction and without assuming the purity of the target state. Last, in order to try to lead back our simulations to realistic experiments, we prove the noise resistance of the characterization and rebuilding of the state.