Many areas of physics rely upon adiabatic state transfer protocols, allowing
a quantum state to be moved between different physical systems for storage and
retrieval or state manipulation. However, these state-transfer protocols suffer
from dephasing and dissipation. In this thesis we go beyond the standard
open-systems treatment of quantum dissipation allowing us to consider
non-Markovian environments. We use adiabatic perturbation theory in order to
give analytic descriptions for various quantum state-transfer protocols. The

Quantum teleportation uses prior shared entanglement and classical
communication to send an unknown quantum state from one party to another.
Remote state preparation (RSP) is a similar distributed task in which the
sender knows the entire classical description of the state to be sent. (This
may also be viewed as the task of non-oblivious compression of a single sample
from an ensemble of quantum states.) We study the communication complexity of
approximate remote state preparation, in which the goal is to prepare an

In quantum interaction problems with explicitly time-dependent interaction
Hamiltonians, the time ordering plays a crucial role for describing the quantum
evolution of the system under con- sideration. In such complex scenarios, exact
solutions of the dynamics are rarely available. Here we study the nonlinear
vibronic dynamics of a trapped ion, driven in the resolved sideband regime with
some small frequency mismatch. By describing the pump field in a quantized

We present a bi-confluent Heun potential for the Schr\"odinger equation
involving inverse fractional powers and a repulsive centrifugal-barrier term
the strength of which is fixed to a constant. This is an infinite potential
well defined on the positive half-axis. Each of the fundamental solutions for
this conditionally integrable potential is written as an irreducible linear
combination of two Hermite functions of a shifted and scaled argument. We
present the general solution of the problem, derive the exact energy spectrum

The mainstream textbooks of quantum mechanics explains the quantum state
collapses into an eigenstate in the measurement, while other explanations such
as hidden variables and multi-universe deny the collapsing. Here we propose an
ideal thinking experiment on measuring the spin of an electron with 3 steps. It
is simple and straightforward, in short, to measure a spin-up electron in
x-axis, and then in z-axis. Whether there is a collapsing predicts different
results of the experiment. The future realistic experiment will show the

We prove spatial decay estimates on disorder-averaged position-momentum
correlations in a gapless class of random oscillator models. First, we prove a
decay estimate on dynamic correlations for general eigenstates with a bound
that depends on the magnitude of the maximally excited mode. Then, we consider
the situation of a quantum quench. We prove that the full time-evolution of an
initially chosen (uncorrelated) product state has disorder-averaged
correlations which decay exponentially in space, uniformly in time.

The Kronig-Penney model, an exactly solvable one-dimensional model of crystal
in solid physics, shows how the allowed and forbidden bands are formed in
solids. In this paper, we study this model in the presence of both strong
spin-orbit coupling and the Zeeman field. We analytically obtain four
transcendental equations that represent an implicit relation between the energy
and the Bloch wavevector. Solving these four transcendental equations, we
obtain the spin-orbital bands exactly. In addition to the usual band gap opened

It is NP-complete to find non-negative factors $W$ and $H$ with fixed rank
$r$ from a non-negative matrix $X$ by minimizing $\|X-WH^\top\|_F^2$. Although
the separability assumption (all data points are in the conical hull of the
extreme rows) enables polynomial-time algorithms, the computational cost is not
affordable for big data. This paper investigates how the power of quantum
computation can be capitalized to solve the non-negative matrix factorization

A simple classical non-local dynamical system with random initial conditions
and an output projecting the state variable on selected axes has been defined
to mimic a two-channel quantum coincidence experiment. Non-locality is
introduced by a parameter connecting the initial conditions to the selection of
the projection axes. The statistics of the results shows violations up to 100%
of the Bell's inequality, in the form of Clauser-Horne- Shimony-Holt (CHSH),
strongly depending on the non-locality parameter. Discussions on the

This tutorial article provides a concise and pedagogical overview on
negatively-charged nitrogen-vacancy (NV) centers in diamond. The research on
the NV centers has attracted enormous attention for its application to quantum
sensing, encompassing the areas of not only physics and applied physics but
also chemistry, biology and life sciences. Nonetheless, its key technical
aspects can be understood from the viewpoint of magnetic resonance. We focus on
three facets of this ever-expanding research field, to which our viewpoint is