Related papers: Structured Unitary Matrices and Quantum Entangleme…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of…
We give an introduction to the theory of multi-partite entanglement. We begin by describing the "coordinate system" of the field: Are we dealing with pure or mixed states, with single or multiple copies, what notion of "locality" is being…
We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…
We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…
In this PhD thesis, several aspects regarding maximal entanglement are analyzed. In the first chapter, Bell Inequalities are analyzed from an operational perspective as well as novel Bell inequalities are obtained together with their…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
We explore the structure of multipartite quantum systems which are entangled in multiple degrees of freedom. We find necessary and sufficient conditions for the characterization of tripartite systems and necessary conditions for any number…
One of the key manifestations of quantum mechanics is the phenomenon of quantum entanglement. While the entanglement of bipartite systems is already well understood, our knowledge of entanglement in multipartite systems is still limited.…
A concise introduction to quantum entanglement in multipartite systems is presented. We review entanglement of pure quantum states of three--partite systems analyzing the classes of GHZ and W states and discussing the monogamy relations.…
In order to use quantum devices for computations, it is necessary to understand the intricacies of the theoretical description. To this end, we provide several novel constructions useful for the comprehension of quantum mechanics from the…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
We present a method to detect entanglement partitions of multipartite quantum systems, by exploiting their inherent symmetries. Structures like genuinely multipartite entanglement, $m$-separability and entanglement depth are detected as…
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…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally…
We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the…
Quantum technologies are enjoying an unprecedented popularity, and some applications are already in the market. This thesis studies two phenomena that are behind a lot of quantum technologies: entanglement and nonlocality. We focus on…
We investigate the entanglement properties of multiparticle systems, concentrating on the case where the entanglement is robust against disposal of particles. Two qubits -belonging to a multipartite system- are entangled in this sense iff…