The last years have seen notable advances in quantum technologies, consolidating the development of basic requirements for the deployment of future quantum networks. Such networks are essential to distributed quantum information applications, and may serve various purposes, e.g., enabling the transmission of quantum states between physically distant parties, or improving the computational capabilities of quantum computers by combining multiple quantum processors. When only local operations and classical communication (LOCC) are allowed, the initial quantum state shared between the parties plays a key role, and may both enable specific applications, or provide the means to answer unsettled theoretical questions.
This PhD project aims at exploring k-stabilizer universal quantum states, that is, n-qubit quantum states that allow inducing any stabilizer state on any subset of k qubits, by using LOCC protocols only. Stabilizer states can be described, up to local unitaries, by the formalism of graph states, representing one of the most important classes of multipartite entanglement, and a powerful resource for many multipartite quantum protocols. The goal of the thesis is threefold. A first objective is to develop deterministic methods to construct k-stabilizer universal graph states on a number of qubits n quadratic in k (theoretical bound), thus improving the scalability and efficiency with respect to current state of the art. A second objective is to investigate the robustness of the derived protocol, for preparing a desired quantum stabilizer state on a subset of k qubits, to potential threats posed by malicious parties or qubit losses. Finally, the last objective of the thesis is to identify connections and implications between k-stabilizer universal graph states, robustness, and quantum error correction, as a way to devise new constructions of quantum error correcting codes of independent interest, or to increase the reliability of quantum networks.