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Entanglement witness is a Hermitian operator that is useful for detecting the genuine multipartite entanglement of mixed states. Nonlinear entanglement witnesses have the advantage of a wider detection range in the entangled region. We…
We explain several separability criteria which rely on uncertainty relations. For the derivation of these criteria uncertainty relations in terms of variances or entropies can be used. We investigate the strength of the separability…
A new criterion necessary and sufficient for the separability of pure bipartite systems for arbitrary finite dimensions is demonstrated; and the corresponding finer quantitative measures or characterizations of entanglement (beyond mere…
We derive a hierarchy of continuous-variable multipartite entanglement conditions in terms of second-order moments of position and momentum operators that generalizes existing criteria. Each condition corresponds to a convex optimization…
Coherent enhancement is a powerful mechanism for improving the sensitivity of a wide range of detectors, but its practical use is often limited by the difficulty of preparing the required quantum states. We show that this difficulty has a…
Recently, a toolkit of highly symmetric techniques employing matrix inequalities has been developed to detect entanglement in various ways. Here we unifiedly explain in detail these methods, and expand them to a new family of positive maps…
We apply the Walborn [Walborn S P, Taketani B G, Salles A, Toscano F and de Matos Filho R L 2009 Entropic Entanglement Criteria for Continuous Variables Phys. Rev. Lett. 103 160505] Shannon Entropic Entanglement Criterion (SEEC), to simple…
A new criterium to detect the entanglement present in a {\it hyperentangled state}, based on the evaluation of an entanglement witness, is presented. We show how some witnesses recently introduced for graph states, measured by only two…
We introduce a general scheme to detect various multiparticle entanglement structures from global non-permutationally invariant observables. In particular, we derive bounds on the variance of non-permutationally invariant and collective…
We construct three-qubit entanglement witnesses with relatively simple structures. Despite their simplicity, these witnesses are capable of detecting a number of bound entangled states more effectively. To illustrate this, two families of…
We study families of positive and completely positive maps acting on a bipartite system $\mathbb{C}^M\otimes \mathbb{C}^N$ (with $M\leq N$). The maps have a property that when applied to any state (of a given entanglement class) they result…
Entanglement is a key resource to demonstrate quantum advantage over classical strategies. Entanglement in quantum states is one of the most well-explored areas in quantum physics. However, a rigorous approach to understanding and detecting…
We propose new entanglement measures as the detection performance based on the hypothesis testing setting. We clarify how our measures work for detecting an entangled state by extending the quantum Sanov theorem. Our analysis covers the…
We present in detail a statistical approach for the reference-frame-independent detection and characterization of multipartite entanglement based on moments of randomly measured correlation functions. We start by discussing how the…
Entanglement, which is an essential characteristic of quantum mechanics, is the key element in potential practical quantum information and quantum communication systems. However, there are many open and fundamental questions (relating to…
The phenomenon of quantum entanglement underlies several important protocols that enable emerging quantum technologies. Entangled states, however, are extremely delicate and often get perturbed by tiny fluctuations in their external…
We propose a new approach to the problem of defining the degree of entanglement between two particles in a pure state with Hilbert spaces of arbitrary finite dimensions. The central idea is that entanglement gives rise to correlations…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
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 introduce a framework for the study of multiparty entanglement by analyzing the behavior of collective variables. Throughout the manuscript, we explore a specific type of multiparty entanglement which can be detected through the…