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The characterization of high-dimensional entanglement plays a crucial role in the field of quantum information science. Conventional entanglement criteria measuring coherent superpositions of multiple basis states face experimental…
Multipartite entanglement detection is crucial for the develop of quantum information science and quantum computation, communication, simulation and metrology tasks. In contrast to experiments, where several handreds of qubits have been…
The Schmidt number characterizes the quantum entanglement of a bipartite mixed state and plays a significant role in certifying entanglement of quantum states. We derive a Schmidt number criterion based on the trace norm of the correlation…
The dimensionality of entanglement is a core tenet of quantum information processing, especially quantum communication and computation. While it is natural to think of this dimensionality in finite dimensional systems, many of the…
A profound comprehension of quantum entanglement is crucial for the progression of quantum technologies. The degree of entanglement can be assessed by enumerating the entangled degrees of freedom, leading to the determination of a parameter…
We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on…
Characterizing entanglement is central for quantum information science. Special observables which indicate entanglement, so-called entanglement witnesses, are a widely used tool for this task. The construction of these witnesses typically…
Entanglement is the hallmark of quantum physics, yet its characterization in interacting many-body systems at thermal equilibrium remains one of the most important challenges in quantum statistical physics. We prove that the Gibbs state of…
Characterizing entanglement of systems composed of multiple particles is a very complex problem that is attracting increasing attention across different disciplines related to quantum physics. The task becomes even more complex when the…
The Schmidt number represents the genuine entanglement dimension of a bipartite quantum state. We derive simple criteria for the Schmidt number of a density matrix in arbitrary local dimensions. They are based on the trace norm of…
Quantum entanglement is an important resource in many modern technologies, like quantum computation or quantum communication and information processing. Therefore, most interest is given to detect and quantify entangled states. Entanglement…
Covariance matrices are a useful tool to investigate correlations and entanglement in quantum systems. They are widely used in continuous variable systems, but recently also for finite dimensional systems powerful entanglement criteria in…
Quantum entanglement has been identified as a crucial concept underlying many intriguing phenomena in condensed matter systems, such as topological phases or many-body localization. Recently, instead of considering mere quantifiers of…
We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. Experimentally quantifying entanglement is highly desired for applications of quantum simulation experiments to fundamental…
Understanding the distribution of quantum entanglement over many parties is a fundamental challenge of quantum physics and is of practical relevance for several applications in the field of quantum information. Here we use methods from…
The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
We present several measurement schemes for accessing separability criteria for continuous-variable bipartite quantum systems. Starting from moments of the bosonic mode operators, criteria suitable to witness entanglement are expressed in…
We introduce a measure of average dimensionality (or coherence) for high-dimensional quantum devices. This includes sets of quantum measurements, steering assemblages, and quantum channels. For measurements and channels, our measure…
In this thesis we study the behavior of bipartite entanglement of a large quantum system, by analyzing the distribution of the Schmidt coefficients of the reduced density matrix. Applying the general methods of classical statistical…