Related papers: Structured Unitary Matrices and Quantum Entangleme…
We review aspects of entanglement entropy in the quantum mechanics of $N\times N$ matrices, i.e. matrix quantum mechanics (MQM), at large $N$. In doing so we review standard models of MQM and their relation to string theory, D-brane…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…
The characterization of quantum correlations is crucial to the development of new quantum technologies and to understand how dramatically quantum theory departs from classical physics. Here we systematically study single- and multiparticle…
We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow to detect the entanglement…
We analyze tight informationally complete measurements for arbitrarily large multipartite systems and study their configurations of entanglement. We demonstrate that tight measurements cannot be exclusively composed neither of fully…
This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to…
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and…
Quantum entanglement plays an important role in quantum computation and communication. It is necessary for many protocols and computations, but causes unexpected disturbance of computational states. Hence, static analysis of quantum…
We study the entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to…
We review and generalize the recently introduced framework of entropy vectors for detecting and quantifying genuine multipartite entanglement in high dimensional multicomponent quantum systems. We show that these ideas can be extended to…
Quantum entanglement is a key resource in quantum computing and quantum information processing tasks. However, its quantification remains a major challenge since it cannot be directly extracted from physical observables. To address this…
PhD thesis dealing with various aspects of multipartite entanglement, such as entanglement measures, absolutely maximally entangled states, bell inequalities, entanglement spectrum and quantum frustration. Also some quantum algorithms run…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
Suppose we have an unknown multipartite quantum state, how can we experimentally find out whether it is genuine multipartite entangled or not? Recall that even for a bipartite quantum state whose density matrix is known, it is already…
We use open quantum system techniques to construct one-parameter semigroups of positive maps and apply them to study the entanglement properties of a class of 16-dimensional density matrices, representing states of a 4x4 bipartite system.
The growth in the demand for precisely crafted many-body systems of spin-$1/2$ particles/qubits is due to their top-notch versatility in application-oriented quantum-enhanced protocols and the fundamental tests of quantum theory. Here we…
Quantum entanglement plays a crucial role in quantum information processing tasks and quantum mechanics, hence quantifying unknown entanglement is a fundamental task. However, this is also challenging, as entanglement cannot be measured by…
Entanglement is a fundamental aspect of quantum physics, both conceptually and for its many applications. Classifying an arbitrary multipartite state as entangled or separable -- a task referred to as the separability problem -- poses a…
The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices,…
Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum…