Entangled state stabilization by local couplings through reservoir-engineering methods ; Méthodes de reservoir-engineering appliquées à la stabilisation de systèmes quantiques multipartites

This thesis aims to use techniques of reservoir engineering in order to stabilize systems of N qubits, with N potentially big, and to develop the tools for the performance analysis of such stabilization.Quantum systems can be used to process information in ways not achievable by classical means. Those systems can be used to perform quantum computation, which is the current ultimate practical goal of quantum information technology, i.e. building a quantum computer. The promise of quantum technology hinges on the ability to precisely control and manipulate the values --- both magnitudes and phases --- in the superposition of basis states. The big challenge is that these values are very sensitive to any spurious signals and couplings to its environment, such that they naturally get progressively blurred; this process is called decoherence. One way to fight decoherence is measurement and feedback action, but the interaction that this constantly involves with the classical world involves design complications and delays. An alternative control approach for quantum state stabilization is quantum reservoir engineering: a dissipative ancilla system (reservoir) and its interaction with the system of interest are designed in such a way that they stabilize the system without any need for external interventions.The first part of this thesis develops several proposals about an application of local reservoir engineering to stabilize an especially delocalized state, namely a GHZ state, which is an entangled state with the characteristic that the ``quantum phase'' information is lost as soon as one subsystem's phase is blurred.The main idea is to combine a scheme periodically resetting the whole system to the particular state |++.+> with an existing conditional stabilization scheme, where the system converges towards the GHZ state if each qubit is initialized in the particular state |++.+>. We examine several ways to implement the synchronization between these two stabilization procedures with local couplings, either by ...