• decoherence
• Majorana
• dissipation
• memories
• quantum information

In order to harness the informational power of quantum physics, one must be able to overcome the challenge of decoherence. Decoherence is an ubiquitous effect arising from the interaction of a quantum system with its environment. Such interactions generally spoil the quantum coherence of the system, thus degrading its information content.

This Thesis deals with the general problem of fighting decoherence in quantum memories. Quantum memories are systems in which a quantum bit can be stored reliably over long periods of time; they represent a necessary intermediate step towards the realization of fully functional quantum computers.

The main focus of the Thesis is on the application of quantum recovery operations to this general problem. A recovery operation is a physical evolution that tries to undo the effect of a previous noise. Even though decoherence processes are generally irreversible, part of the information that is removed from the original encoding subspace may still be recoverable from other regions of the state space of the memory. Thus, by applying a suitable recovery operation, the fidelity between the encoded state and the recovered one can be improved. By optimizing over all physical recovery operations, a reliable measure for the performance of the quantum memory can be defined.

The Thesis is structured as follows. After an introduction to the fundamental concepts in quantum information theory, we define recovery operations and present some results about them, including an upper bound on the optimal recovery fidelity that can be used to evaluate the performance of quantum memory models. We then discuss an application of these concepts, which exploits a suitably engineered form of dissipation to implement a continuous-time version of quantum error correction. Then, after a discussion on how Hamiltonians can be used to protect quantum information, we turn to a second application, which is based on unpaired Majorana modes in condensed matter systems. These exotic quasi-particles have some remarkable properties that suggest they could be used to store quantum information in a way that is immune from local perturbations. We discuss the performance of Majorana-based quantum memories in the open-system scenario, using analytically solvable toy models, and focus on how the results relate to the concepts of locality and parity, which are generally assumed to underpin the efficacy of Majorana-based quantum memories. In the last Chapter, we remark on the importance of recovery operations in the study of quantum memories and on some interesting open problems about dissipation-based and Majorana-based quantum memories.