Related papers: Separability criteria and bounds for entanglement …
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…
Great advances have been achieved in studying characteristics of entanglement for fundamentals of quantum mechanics and quantum information processing. However, even for N-qubit systems, the problem of entanglement criterion has not been…
In this paper, we give out some effective criterions which can be used to judge the separability of multipartite pure states. We obtain the relationship between separability and Schmidt decomposable of multipartite pure states in Theorem1.…
The concept of entanglement is at the core of the theory of quantum information. In this paper a criterion for unentanglement of quantum states is proposed and proved. This criterion is natural, practical and easy to check.
It is known that realignment crierion is necessary but not a sufficient criterion for lower as well as higher dimensional system. In this work, we first consider a two-qubit system and derived the necessary and sufficient condition based on…
A key requirement of any separable quantum state is that its density matrix has a positive partial transpose. For continuous bipartite quantum states, violation of this condition may be tested via the hierarchy of negative-partial-transpose…
We propose in this work a practical approach to address the longstanding and challenging problem of quantum separability, leveraging the correlation matrices of generic observables. General separability conditions are obtained by dint of…
Entanglement detection problem is one of the important problem in quantum information theory. Gurvit showed that this problem is NP complete and thus this may be the possible reason that only one criterion is not sufficient to detect all…
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…
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 provide a canonical form of mixed states in bipartite quantum systems in terms of a convex combination of a separable state and a, so-called, edge state. We construct entanglement witnesses for all edge states. We present a canonical…
Explicit sufficient and necessary conditions for separability of $N$-dimensional rank two multiparty quantum mixed states are presented. A nonseparability inequality is also given, for the case where one of the eigenvectors corresponding to…
We derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system. The main ingredient of the presented derivation is the triangle inequality applied to the root…
Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and…
We investigate the Peres-Horodecki positive partial transpose (PPT) criterion in the context of conserved quantities and derive a condition of in- separability for a composite bipartite system depending only on the dimen- sions of its…
For a given Hamiltonian $H$ on a multipartite quantum system, one is interested in finding the energy $E_0$ of its ground state. In the separability approximation, arising as a natural consequence of measurement in a separable basis, one…
We consider the separability of rank two quantum states on multiple quantum spaces with different dimensions. The sufficient and necessary conditions for separability of these multiparty quantum states are explicitly presented. A…
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 develop separability criteria to identify non-$k$-separability $(k = 2,3,\ldots,n)$ and genuine multipartite entanglement in different classes of mixed $n$-partite quantum states using elements of density matrices. With the help of these…
We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.