Related papers: Entanglement and Quantum Groups
We examine several well known quantum spin models and categorize behavior of pairwise entanglement at quantum phase transitions. A unified picture on the connection between the entanglement and quantum phase transition is given.
I present a new group-theoretical approach to the interaction mechanism of elementary particle physics. Within an irreducible unitary two-particle representation of the Poincare group, the commutation relations of the Poincare group require…
We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be…
Neven et al. have explored an unexpected alliance between the mathematical insights of Sir Isaac Newton and Ren\'e Descartes which culminates in the reduction of the Positive Partial Transpose (PPT) criterion to an equivalent hierarchy of…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
Inspired by its fundamental importance in quantum mechanics, we define and study the notion of entanglement for abstract physical theories, investigating its profound connection with the concept of superposition. We adopt the formalism of…
In this paper, we initiate a systematic study of entanglements of division fields from a group theoretic perspective. For a positive integer $n$ and a subgroup $G\subseteq \text{GL}_2(\mathbb{Z}/{n}\mathbb{Z})$ with surjective determinant,…
The present Thesis covers the subject of the characterization of entangled states by recourse to entropic measures, as well as the description of entanglement related to several issues in quantum mechanics, such as the speed of a quantum…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
By the topological argument that the identity matrix is surrounded by a set of separable states follows the result that if a system is entangled at thermal equilibrium for some temperature, then it presents a phase transition (PT) where…
In this paper, we provide a complete mathematical theory for the entanglement of mixtures of Dicke states. These quantum states form an important subclass of bosonic states arising in the study of indistinguishable particles. We introduce a…
We investigate the structure of SO(3)-invariant quantum systems which are composed of two particles with spins j_1 and j_2. The states of the composite spin system are represented by means of two complete sets of rotationally invariant…
In this paper, we expose the construction of a possible, simple quantum matrix group (according to Woronowicz), related to elementary formal aspects of the Einstein field equations of General Relativity, and its possible symmetries.
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…
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
We present here a set of lecture notes on quantum thermodynamics and canonical typicality. Entanglement can be constructively used in the foundations of statistical mechanics. An alternative version of the postulate of equal a priori…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…
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. In…
Quantum entanglement was first recognized as a feature of quantum mechanics in the famous paper of Einstein, Podolsky and Rosen [18]. Recently it has been realized that quantum entanglement is a key ingredient in quantum computation,…