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The Aharanov-Bohm (AB) effect, which predicts that a magnetic field strongly

influences the wave function of an electrically charged particle, is

investigated in a three site system in terms of the quantum control by an

additional dephasing source. The AB effect leads to a non-monotonic dependence

of the steady-state current on the gauge phase associated with the molecular

ring. This dependence is sensitive to site energy, temperature, and dephasing,

and can be explained using the concept of the dark state. Although the phase

Suppressing undesired non-unitary effects in a quantum system is a major

challenge in quantum computation and quantum control. In this scenario, the

investigation of the adiabatic dynamics under decoherence allows for optimal

strategies in adiabatic protocols in the presence of a surrounding environment.

In this work, we address this point by theoretically and experimentally

analyzing the robustness of the adiabatic theorem in open quantum systems. More

The ZX-Calculus is a graphical language for diagrammatic reasoning in quantum

mechanics and quantum information theory. It comes equipped with an equational

presentation. We focus here on a very important property of the language:

completeness, which roughly ensures the equational theory captures all of

quantum mechanics. We first improve on the known-to-be-complete presentation or

the so-called Clifford fragment of the language - a restriction that is not

universal - by adding some axioms. Thanks to a system of back-and-forth

A phenomenological construction of quantum Langevin equations, based on the

physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo

formula, (iii) the virial theorem and (iv) the quantum fluctuation-dissipation

theorem is presented. The case of a single harmonic oscillator coupled to a

large external bath is analysed in detail. This allows to distinguish a

markovian semi-classical approach, due to Bedeaux and Mazur, from a

non-markovian full quantum approach, due to to Ford, Kac and Mazur. The

We demonstrate the preparation and coherent control of the angular momentum

state of a two-ion crystal. The ions are prepared with an average angular

momentum of $7780\hbar$ freely rotating at 100~kHz in a circularly symmetric

potential, allowing us to address rotational sidebands. By coherently exciting

these motional sidebands, we create superpositions of states separated by up to

four angular momentum quanta. Ramsey experiments show the expected dephasing of

An outstanding goal in quantum optics and scalable photonic quantum

technology is to develop a source that each time emits one and only one

entangled photon pair with simultaneously high entanglement fidelity,

extraction efficiency, and photon indistinguishability. By coherent two-photon

excitation of a single InGaAs quantum dot coupled to a circular Bragg grating

bullseye cavity with broadband high Purcell factor up to 11.3, we generate

entangled photon pairs with a state fidelity of 0.90(1), pair generation rate

A new proof of the Weyl limit point-limit circle criterion is obtained, with

systematic emphasis on Sobolev-space methods.

Percolation theory allows simple description of the phase transition based on

the scaling properties of the network clusters with respect to a single

parameter - site or bond occupation probability. How to design a network

exhibiting the percolation transition for a chosen occupation probability has

been an open problem. At the same time, the task to find a structurally simple

network having the desired property seemed to be impossible. I suggest a model,

where the combination of the classical and the quantum resources creates a

We consider the quantum partition function for a system of quantum spinors

and then derive an equivalent (or dual) classical partition function for some

scalar degrees of freedom. The coupling between scalars is non-trivial (e.g. a

model on 2-sphere configuration space), but the locality structure of the dual

system is preserved, in contrast to the imaginary time formalism. We also show

that the measure of integration in the classical partition function can be

The Caldeira-Leggett master equation as an example of Markovian master

equation without Lindblad form is investigated for mathematical consistency. We

explore situations both analytically and numerically where the positivity

violations of the density operator occur. We reinforce some known knowledge

about this problem but also find new surprising cases. Our analytical results

are based on the full solution of the Caldeira-Leggett master equation obtained

via the method of characteristics. The preservation of positivity is mainly