This thesis is devoted to the study of coherent storage of quantum information as well as its potential applications. Quantum memories are crucial to harnessing the potential of quantum physics for information processing tasks. They are required for almost all quantum computation proposals. However, despite the large arsenal of theoretical techniques and proposals dedicated to their implementation, the realization of long-lived quantum memories remains an elusive task. Encoding information in quantum states associated to many-body topological phases of matter and protecting them by means of a static Hamiltonian is one of the leading proposals to achieve quantum memories. While many genuine and well publicized virtues have been demonstrated for this approach, equally real limitations were widely disregarded. In the first two projects of this thesis, we study limitations of passive Hamiltonian protection of quantum information under two different noise models. Chapter 2 deals with arbitrary passive Hamiltonian protection for a many body system under the effect of local depolarizing noise. It is shown that for both constant and time dependent Hamiltonians, the optimal enhancement over the natural single-particle memory time is logarithmic in the number of particles composing the system. The main argument involves a monotonic increase of entropy against which a Hamiltonian can provide little protection. Chapter 3 considers the recoverability of quantum information when it is encoded in a many-body state and evolved under a Hamiltonian composed of known geometrically local interactions and a weak yet unknown Hamiltonian perturbation. We obtain some generic criteria which must be fulfilled by the encoding of information. For specific proposals of protecting Hamiltonian and encodings such as Kitaev’s toric code and a subsystem code proposed by Bacon, we additionally provide example perturbations capable of destroying the memory which imply upper bounds for the provable memory times.