Quantum memory

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. Chapter 4 proposes engineered
dissipation as a natural solution for continuously extracting the
entropy introduced by noise and keeping the accumulation of errors
under control. Persuasive evidence is provided supporting that
engineered dissipation is capable of preserving quantum degrees of
freedom from all previously considered noise models. Furthermore,
it is argued that it provides additional flexibility over
Hamiltonian thermalization models and constitutes a promising
approach to quantum memories. Chapter 5 introduces a particular
experimental realization of coherent storage, shifting the focus in
many regards with respect to previous chapters. First of all, the
system is very concrete, a room-temperature nitrogen-vacancy centre
in diamond, which is subject to actual experimental control and
noise restrictions which must be adequately modelled. Second, the
relevant degrees of freedom reduce to a single electronic spin and
a carbon 13 spin used to store a qubit. Finally, the approach taken
to battle decoherence consists of inducing motional narrowing and
applying dynamical decoupling pulse sequences, and is tailored to
address the systems dominant noise sources. Chapter 6 analyses
unforgeable tokens as a potential application of these
room-temperature qubit memories. Quantum information protocols
based on Wiesner's quantum money scheme are proposed and analysed.
We provide the first rigorous proof that such unentangled tokens
may be resistant to counterfeiting attempts while tolerating a
certain amount of noise. In summary, this thesis provides
contributions to quantum memories in four different aspects. Two
projects were dedicated to understanding and exposing the
limitations of existing proposals. This is followed by a
constructive proposal of a new counter-intuitive theoretical model
for quantum memories. An applied experimental project achieves
record coherent storage times in room-temperature solids. Finally,
we provide rigorous analysis for a quantum information application
of quantum memories. This completes a broad picture of quantum
memories which integrates different perspectives, from theoretical
critique and constructive proposal, to technological application
going through a down-to-earth experimental implementation.