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We report the creation of a wide range of quantum states with controllable degrees of entanglement and entropy using an optical two-qubit source based on spontaneous parametric downconversion. The states are characterised using measures of…

Using the semigroup approach to abstract boundary control problems we characterize the space of all exactly reachable states. Moreover, we study the situation when the controls of the system are required to be positive. The abstract results…

Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…

Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…

This paper provides a framework for the control of quantum mechanical systems with scattering states, i.e., systems with continuous spectra. We present the concept and prove a criterion of the approximate strong smooth controllability. Our…

This work seeks to make explicit the operational connection between the preparation of two-level quantum systems with their corresponding description (as states) in a Hilbert space. This may sound outdated, but we show there is more to this…

The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…

Topology is an important degree of freedom in characterizing electronic systems. Recently, it also brings new theoretical frontiers and many potential applications in photonics. However, the verification of the topological nature is highly…

Coherent transport of atoms trapped in an optical lattice can be controlled by microwave-induced spin flips that correlate with site-to-site hopping. We study the controllability of homogeneous one-dimensional systems of noninteracting…

The identification, description, and classification of topological features is an engine of discovery and innovation in several fields of physics. This research encompasses a broad variety of systems, from the integer and fractional Chern…

We consider quantum state tomography with measurement procedures of the following type: First, we subject the quantum state we aim to identify to a know time evolution for a desired period of time. Afterwards we perform a measurement with a…

Quantum control refers to our ability to manipulate quantum systems. This tutorial-style chapter focuses on the use of classical electromagnetic fields to steer the system dynamics. In this approach, the quantum nature of the control stems…

Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some…

We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…

This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…

We study the dynamics of states perturbatively expanded about a harmonic system of loop quantum cosmology, exhibiting a bounce. In particular, the evolution equations for the first and second order moments of the system are analyzed. These…

The finite-time control problem of quantum systems is investigated in this paper. We first define finite-time stability and present a finite-time Lyapunov stability criterion for finite-dimensional quantum systems in coherence vector…

A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…

We present a review on the progress in the understanding and characterization of holonomy and topology of a discrete-time quantum walk architecture, consisting of a unitary step given by a sequence of two non-commuting rotations in…

In this work we present a model qubit whose basis states are eigenstates of a multi-layered quantum dot. We show that the proper design of the quantum dot results in qubit states that have excellent dynamical properties when a…