Related papers: Conditions for entanglement in multipartite system…
We provide a class of inequalities for detecting entanglements in multi-mode systems. Necessary conditions for fully separable, bi-separable and sufficient conditions for fully entangled states are explicitly presented.
We provide a class of inequalities whose violation shows the presence of entanglement in two-mode systems. We initially consider observables that are quadratic in the mode creation and annihilation operators and find conditions under which…
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…
We review the problem of discriminating entangled states from separable states for bipartite systems. We formally define what entangled states are, present some important criteria to detect entanglement, and show how they can be classified…
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…
Necessary and sufficient conditions for bipartite entanglement are derived, which apply to arbitrary Hilbert spaces. Motivated by the concept of witnesses, optimized entanglement inequalities are formulated solely in terms of arbitrary…
The variety of multi-partite entangled states enables numerous applications in novel quantum information tasks. In order to compare the suitability of different states from a theoretical point of view classifications have been introduced.…
We present an inequality for detecting entanglement and distillability of arbitrary dimensional bipartite systems. This inequality provides a sufficient condition of entanglement for bipartite mixed states, and a necessary and sufficient…
We discuss the problem of determining whether the state of several quantum mechanical subsystems is entangled. As in previous work on two subsystems we introduce a procedure for checking separability that is based on finding state…
A system of three or four particle can be entangled in a number of different ways. It may be the case that only subsets of the particles are entangled, and these subsets are not entangled with each other. It may also be the case that the…
Necessary and sufficient observable conditions for the nonnegativity of all partial transpositions of multi-mode quantum states are derived. The result is a hierarchy of inequalities for minors in terms of moments of the given state.…
We introduce an operational procedure to determine, with arbitrary probability and accuracy, optimal entanglement witness for every multipartite entangled state. This method provides an operational criterion for separability which is…
Based on the generators of $SU(n)$ we present inequalities for detecting quantum entanglement for $2 \otimes d$ and $M \otimes N$ systems. These inequalities provide a sufficient condition of entanglement for bipartite mixed states and give…
We provide necessary and sufficient conditions for the partial transposition of bipartite harmonic quantum states to be nonnegative. The conditions are formulated as an infinite series of inequalities for the moments of the state under…
We present a review of the problem of finding out whether a quantum state of two or more parties is entangled or separable. After a formal definition of entangled states, we present a few criteria for identifying entangled states and…
Multipartite entanglement is very poorly understood despite all the theoretical and experimental advances of the last decades. Preparation, manipulation and identification of this resource is crucial for both practical and fundamental…
Entanglement witnesses provide tools to detect entanglement in experimental situations without the need of having full tomographic knowledge about the state. If one estimates in an experiment an expectation value smaller than zero, one can…
We present a way of identifying all kinds of entanglement for three-qubit pure states in terms of the expectation values of Pauli operators. The necessary and sufficient conditions to classify the fully separable, biseparable, and genuine…
We explore the structure of multipartite quantum systems which are entangled in multiple degrees of freedom. We find necessary and sufficient conditions for the characterization of tripartite systems and necessary conditions for any number…
A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite…