Related papers: Improved Separability Criteria Based on Bloch Repr…
We review the criteria for separability and quantum entanglement, both in a bipartite as well as a multipartite setting. We discuss Bell inequalities, entanglement witnesses, entropic inequalities, bound entanglement and several features of…
We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be…
We explore the subtle relationships between partial separability and entanglement of subsystems in multiqubit quantum states and give experimentally accessible conditions that distinguish between various classes and levels of partial…
We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a…
A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. Every symmetric operator, represented by a symmetric matrix with only two nonzero elements, and their…
Inspired by the realignment or computable cross norm criterion, we present a new result about the characterization of quantum entanglement. Precisely, an interesting class of inequalities satisfied by all separable states of a bipartite…
Detecting entanglement in many-body quantum systems is crucial but challenging, typically requiring multiple measurements. Here, we establish the class of states where measuring connected correlations in just $\textit{one}$ basis is…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
The generalized Bloch decomposition of a bipartite quantum state gives rise to a correlation matrix whose singular values provide rich information about non-local properties of the state, such as the dimensionality of entanglement. While…
We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…
We point out that density matrices can only be used to describe quantum states, so the entanglement contained in a density matrix is just quantum entanglement. This means a bipartite state described by a density matrix contains quantum…
The quantum formalism can be completed by assuming that a density operator can also represent a pure state. An 'extended Bloch representation' (EBR) then results, in which not only states, but also the measurement-interactions can be…
We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We…
Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the…
Explicit sufficient and necessary conditions for separability of higher dimensional quantum systems with rank two density matrices are given. A nonseparability inequality is also presented, for the case where one of the eigenvectors…
We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss…
In this paper, we explore the graphical representation of two-qubit entanglement on two Bloch Spheres via stabilizer formalism. We relate the density matrix to the graphical representation on two Bloch Spheres by showing how both may be…
It is shown that any separable state on Hilbert space ${\cal H}={\cal H}_1\otimes{\cal H}_2$, can be written as a convex combination of N pure product states with $N\leq (dim{\cal H})^2$. Then a new separability criterion for mixed states…
Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using…
We propose a unified mathematical scheme, based on a classical tensor isomorphism, for characterizing entanglement that works for pure states of multipartite systems of any number of particles. The degree of entanglement is indicated by a…