Related papers: Bipartite Entanglement Review of Subsystem-Basis E…
We introduce a class of inequalities based on low order correlations of operators to detect entanglement in bipartite systems. The operators may either be Hermitian or non-Hermitian and are applicable to any physical system or class of…
This article presents the basis of a theory of entanglement. We begin with a classical theory of entangled discrete measures in Section~1. Section~2 treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert…
Necessary and sufficient conditions for bipartite entanglement are derived, which apply to arbitrary Hilbert spaces. Motivated by the concept of witnesses, optimized entanglement inequalities are formulated solely in terms of arbitrary…
We present a new paradigm for capturing the complementarity of two observables. It is based on the entanglement created by the interaction between the system observed and the two measurement devices used to measure the observables…
We present unified approach to different recent entanglement criteria. Although they were developed in different ways, we show that they are all applications of a more general principle given by the Cauchy-Schwarz inequality. We explain…
This thesis poses a selection of recent research of the author in a common context. It starts with a selected review on research concerning the role entanglement might play at quantum phase transitions and introduces measures for…
We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation…
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…
This Dissertation collects my results on the interpretation, characterization, quantification and application of bipartite and multipartite entanglement in Gaussian states of continuous variable systems.
Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract…
Multipartite entanglement is very poorly understood despite all the theoretical and experimental advances of the last decades. Preparation, manipulation and identification of this resource is crucial for both practical and fundamental…
We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system,…
In this letter we discuss a new entanglement measure. It is based on the Hilbert-Schmidt norm of operators. We give an explicit formula for calculating the entanglement of a large set of states on C^2 \times C^2. Furthermore we find some…
Partial trace is a very important mathematical operation in quantum mechanics. It is not only helpful in studying the subsystems of a composite quantum system but also used in computing a vast majority of quantum entanglement measures.…
The paper introduces unbounded antilinear operators on Hilbert spaces and develops their fundamental theory. In particular, we establish a closed range theorem, a polar decomposition theorem, and the convexity of the numerical range for…
Statistical ensembles of reduced density matrices of bipartite quantum systems play a central role in entanglement estimation, but do not capture the non-stationary nature of entanglement relevant to realistic quantum information…
In this PhD thesis we propose an algorithmic approach to the study of the Hilbert scheme. Developing algorithmic methods, we also obtain general results about Hilbert schemes. In Chapter 1 we discuss the equations defining the Hilbert…
We consider the Schmidt decomposition of a bipartite density operator induced by the Hilbert-Schmidt scalar product, and we study the relation between the Schmidt coefficients and entanglement. First, we define the Schmidt equivalence…
Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, $N$. Fortunately, it is still possible to…
Collaboration networks are studied as an example of growing bipartite networks. These have been previously observed to have structure such as positive correlations between nearest-neighbour degrees. However, a detailed understanding of the…