Related papers: Bound entanglement and continuous variables

We present a notion of generalized entanglement which goes beyond the conventional definition based on quantum subsystems. This is accomplished by directly defining entanglement as a property of quantum states relative to a distinguished…

We introduce a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such…

First, we show how the quantum circuits for generating and measuring multi-party entanglement of qubits can be translated to continuous quantum variables. We derive sufficient inseparability criteria for $N$-party continuous-variable states…

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…

Entanglement is a key resource for fundamental tests of physics and emerging quantum technologies. In quantum optics, two perspectives on entanglement coexist. In the continuous-variable framework, entanglement is understood as holding…

We define what it means for a state in a convex cone of states on a space of observables to be generalized-entangled relative to a subspace of the observables, in a general ordered linear spaces framework for operational theories. This…

We outline the basic questions that are being studied in the theory of entanglement. Following a brief review of some of the main achievements of entanglement theory for finite-dimensional quantum systems such as qubits, we will consider…

Among the possibly most intriguing aspects of quantum entanglement is that it comes in "free" and "bound" instances. Bound entangled states require entangled states in preparation but, once realized, no free entanglement and therefore no…

We review the theory of continuous-variable entanglement with special emphasis on foundational aspects, conceptual structures, and mathematical methods. Much attention is devoted to the discussion of separability criteria and entanglement…

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…

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 expected indefinite causal structure in quantum gravity poses a challenge to the notion of entanglement: If two parties are in an indefinite causal relation of being spacelike and timelike, can they still be entangled? If so, how does…

From the physical point of view entanglement witnesses define a universal tool for analysis and classification of quantum entangled states. From the mathematical point of view they provide highly nontrivial generalization of positive…

We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…

Bound entangled states are states that are entangled but from which no entanglement can be distilled if all parties are allowed only local operations and classical communication. However, in creating these states one needs nonzero…

Given an arbitrary statistical theory, different from quantum mechanics, how to decide which are the nonclassical correlations? We present a formal framework which allows for a definition of nonclassical correlations in such theories,…

The positivity of the partial transpose is in general only a necessary condition for separability. There exist quantum states that are not separable, but nevertheless are positive under partial transpose. States of this type are known as…

This note quantifies the continuity properties of entanglement: how much does entanglement vary if we change the entangled quantum state just a little? This question is studied for the pure state entanglement of a bipartite system and for…

An entangled state is bound entangled, if one cannot combine any number of copies of the state to a maximally entangled state, by using only local operations and classical communication. If one formalizes this notion of bound entanglement,…

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…