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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