Related papers: Entanglement conditions and polynomial identities

In this paper we introduce a criterion for the characterization of Entanglement Witness for multipartite quantum systems. Our approach is based on the characterization of the "tangent space" to the set of pure product states.

We introduce a multi-mode squeezing coefficient to characterize entanglement in $N$-partite continuous-variable systems. The coefficient relates to the squeezing of collective observables in the $2N$-dimensional phase space and can be…

In this work, we present a practical and efficient framework for verifying entangled states when only a tomographically incomplete measurement setting is available-specifically, when access to observables is severely limited. We show how…

We present local invariants of multi-partite pure or mixed states, which can be easily calculated and have a straight-forward physical meaning. As an application, we derive a new entanglement criterion for arbitrary mixed states of $n$…

To quantify the entanglement of bipartite systems in terms of some entanglement measure is a challenging problem in general, and it is much worse when the information about the system is less. In this manuscript, based on two classes of…

We derive several entanglement criteria for bipartite continuous variable quantum systems based on the Shannon entropy. These criteria are more sensitive than those involving only second-order moments, and are equivalent to well-known…

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…

Tensor polynomial identities generalize the concept of polynomial identities on $d \times d$ matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their…

Entanglement detection typically relies on linear inequalities for mean values of certain observables (entanglement witnesses), where violation indicates entanglement. We provide a general method to improve any of these inequalities for…

We develop a model in which presence of entanglement in a quantum system can be confirmed through coarse observations of the environment surrounding the system. This counter-intuitive effect becomes possible when interaction between the…

We derive a family of entanglement criteria for continuous variable systems based on the R\'enyi entropy of complementary distributions. We show that these entanglement witnesses can be more sensitive than those based on second-order…

We present a significantly improved scheme of entanglement detection inspired by local uncertainty relations for a system consisting of two qubits. Developing the underlying idea of local uncertainty relations, namely correlations, we…

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…

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…

Let a pure state \psi be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix \rho of an N-dimensional subsystem. The bipartite entanglement properties of \psi are encoded in the spectrum of \rho. By…

We use concepts from quantum cryptography to relate the entanglement in many-body mixed states to standard correlation functions. If a system can be used as a resource for distilling private keys -- random classical bits that are shared by…

The entanglement criterion for continuous variable systems and the conditions under which the uncertainty relations are fulfilled are generalized to the case of a noncommutative (NC) phase-space. The quantum nature and the separability of…

We show that an entanglement measure called relative entropy of entanglement satisfies a strong continuity condition. If two states are close to each other then so are their entanglements per particle pair in this measure. It follows in…

We present a class of entanglement identifiers which has the following experimentally friendly feature: once the expectation value of the identifier exceeds some definite limit, we can conclude the state is entangled, even if not all…

We introduce the concept of entanglement width as measure of the spatial distribution of entanglement in multiparticle systems. We develop criteria to detect the width of entanglement using global observables such as energy and magnetic…