相关论文: A Combinatory-Algebraic Perspective on Multipartit…
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 analyze multipartite entanglement in systems of spin-1/2 particles from a relativistic perspective. General conditions which have to be met for any classification of multipartite entanglement to be Lorentz invariant are derived, which…
In this paper we present several multipartite quantum systems featuring the same type of genuine (tripartite) entanglement. Based on a geometric interpretation of the so-called $|W\rangle$ and $|GHZ\rangle$ states we show that the…
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this…
This paper addresses the following main question: Do we have a theoretical understanding of entanglement applicable to a full variety of physical settings? It is clear that not only the assumption of distinguishability, but also the…
We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…
Quantum entanglement in multipartite systems cannot be shared freely. In order to illuminate basic rules of entanglement sharing between qubits we introduce a concept of an entangled structure (graph) such that each qubit of a multipartite…
The paper contains a brief review of an approach to quantum entanglement based on analysis of dynamic symmetry of systems and quantum uncertainties, accompanying the measurement of mean value of certain basic observables. The latter are…
Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite dimensional subspaces. Hence, entanglement is a finite dimensional property. A generalization for multipartite…
In modern physics only relative quantities are considered to have physical significance. For example, position assigned to a system depends on the choice of coordinates, and only relative distances between different systems have physical…
Quantum Entanglement is one of the key manifestations of quantum mechanics that separate the quantum realm from the classical one. Characterization of entanglement as a physical resource for quantum technology became of uppermost…
Genuine multipartite entanglement is crucial for quantum information and related technologies but quantifying it has been a long-standing challenge. Most proposed measures do not meet the ``genuine'' requirement, making them unsuitable for…
We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.
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…
For many applications the presence of a quantum advantage crucially depends on the availability of resourceful states. Although the resource typically depends on the particular task, in the context of multipartite systems entangled quantum…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…
We introduce algebraic sets in the complex projective spaces for the mixed states in bipartite quantum systems as their invariants under local unitary operations. The algebraic sets of the mixed state have to be the union of the linear…
Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify…
We discuss the concept of how entanglement changes with respect to different factorizations of the total algebra which describes the quantum states. Depending on the considered factorization a quantum state appears either entangled or…
The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states which admit a fully local hidden…