Related papers: Entanglement witnesses: construction, analysis and…
We introduce an approach which allows a detailed structural and quantitative analysis of multipartite entanglement. The sets of states with different structures are convex and nested. Hence, they can be distinguished from each other using…
Entanglement in multipartite systems is a key resource for quantum information and communication protocols, making its verification in complex systems a necessity. Because an exact calculation of arbitrary entanglement probes is impossible,…
Verification of entanglement is an important tool to characterize sources and devices for use in quantum computing and communication applications. In a vast majority of experiments entanglement witnesses (EW) are used in order to prove the…
We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as…
Entanglement witnesses are invaluable for efficient quantum entanglement certification without the need for expensive quantum state tomography. Yet, standard entanglement witnessing requires multiple measurements and its bounds can be…
In this paper we present a new method for entanglement witnesses construction. We show that to construct such an object we can deal with maps which are not positive on the whole domain, but only on a certain sub-domain. In our approach…
We give a universal recipe for constructing nonlinear entanglement witnesses able to detect non-classical correlations in arbitrary systems of distinguishable and/or identical particles for an arbitrary number of constituents. The…
To address the outstanding task of detecting entanglement in large quantum systems, entanglement witnesses have emerged, addressing the separable nature of a state. Yet optimizing witnesses, or accessing them experimentally, often remains a…
A new family of positive, trace-preserving maps is introduced. It is defined using the mutually unbiased measurements, which generalize the notion of mutual unbiasedness of orthonormal bases. This family allows one to define entanglement…
We introduce informationally complete measurements whose outcomes are entanglement witnesses and so answer the question of how many witnesses need to be measured to decide whether an arbitrary state is entangled or not: as many as the…
We provide a class of optimal nondecomposable entanglement witnesses for 4N x 4N composite quantum systems or, equivalently, a new construction of nondecomposable positive maps in the algebra of 4N x 4N complex matrices. This construction…
Genuine multipartite entanglement is arguably the most valuable form of entanglement in the multipartite case, with applications, for instance, in quantum metrology. In order to detect that form of entanglement in multipartite quantum…
In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied…
Motivated by the Peres-Horodecki criterion and the realignment criterion we develop a more powerful method to identify entangled states for any bipartite system through a universal construction of the witness operator. The method also gives…
We provide a generalization of the reduction and Robertson positive maps in matrix algebras. They give rise to a new class of optimal entanglement witnesses. Their structural physical approximation is analyzed. As a byproduct we provide a…
The primary goal of entanglement theory is to determine convertibility conditions for two quantum states. Up until now, this has always been done with the use of entanglement monotones. With the exception of the negativity, such quantities…
We characterize a set of positive maps in matrix algebra of 4x4 complex matrices. Equivalently, we provide a subset of entanglement witnesses parameterized by the rotation group SO(3). Interestingly, these maps/witnesses define two…
We propose a set of linear quantum entanglement witnesses constituted by local quantum-mechanical observables with each two possible measurement outcomes. These witnesses detect all the entangled resources which give rise to a better…
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…
The geometric measure of entanglement is an approach to quantifying entanglement that is based on the Hilbert-space distance (or, equivalently, angle) between pure states and their best unentangled approximants. An entanglement witness is…