Related papers: Separability of N-particle Fermionic States for Ar…

We present a necessary and sufficient product criterion for bipartite quantum states based on the rank of realignment matrix of density matrix. Then, this approach is generalized to multipartite systems. We first introduce the concept of…

Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these…

We study separability criteria in multipartite quantum systems of arbitrary dimensions by using the Bloch representation of density matrices. We first derive the norms of the correlation tensors and obtain the necessary conditions for…

We analyze a general bipartite-like representation of arbitrary pure states of $N$ indistinguishable particles, valid for both bosons and fermions, based on $M$- and $(N-M)$-particle states. It leads to exact $(M,N-M)$ Schmidt-like…

We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein {\it et al.} [Phys. Rev. A \textbf{73}, 012320 (2006)]. The conjecture states…

We obtain a collection of necessary (sufficient) conditions for a bipartite system of qubits to be separable (entangled), which are based on the Landau-Pollak formulation of the uncertainty principle. These conditions are tested, and…

The entanglement detection via local measurements can be experimentally implemented. Based on mutually unbiased measurements and general symmetric informationally complete positive-operator-valued measures, we present separability criteria…

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…

We extend the classification of mixed states of quantum systems composed of arbitrary number of subsystems of arbitrary dimensions. This extended classification is complete in the sense of partial separability and gives 1+18+1 partial…

In a system of $n$ quantum particles, the correlations are classified into a series of irreducible $k$-particle correlations ($2\le k\le n$), where the irreducible $k$-particle correlation is the correlation appearing in the states of $k$…

Quantum coherence, a basic feature of quantum mechanics residing in superpositions of quantum states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical…

We show that for fermion states, measurements of any two finite outcome particle quantum numbers (e.g.\ spin) are not constrained by a minimum total uncertainty. We begin by defining uncertainties in terms of the outputs of a measurement…

We introduce a sufficient and necessary condition for the separability of a specific class of $N$ $d$-dimensional system (qudits) states, namely special generalized Werner state (SGWS): $W^{[d^N]}(v)=(1-v)\frac{I^{(N)}}{d^N}+v|\psi…

In this paper, we present a method to construct full separability criteria for tripartite systems of qubits. The spirit of our approach is that a tripartite pure state can be regarded as a three-order tensor that provides an intuitionistic…

We present a class of non-Gaussian two-mode continuous variable states for which the separability criterion for Gaussian states can be employed to detect whether they are separable or not. These states reduce to the two-mode Gaussian states…

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which…

Identifying the $k$-partite entanglement and $k$-nonseparability of general $N$-partite quantum states are fundamental issues in quantum information theory. By use of computable inequalities of nonlinear operators, we present some simple…

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 derive criteria for $k$-separability of multipartite Quantum state

Unlike for bipartite states consisting of distinguishable particles, in the case of identical parties the notion of entanglement is still under debate. In the following, we review two different approaches to the entanglement of systems…