Related papers: Separability of rank two quantum states on multipl…
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…
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…
Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we…
In this paper, we mainly discuss the separability of $n$-partite quantum states from elements of density matrices. Practical separability criteria for different classes of $n$-qubit and $n$-qudit quantum states are obtained. Some of them…
We investigate the separability of quantum states based on covariance matrices. Separability criteria are presented for multipartite states. The lower bound of concurrence proposed in Phys. Rev. A. 75, 052320 (2007) is improved by…
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…
For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.
One of the most important problems in quantum information is the separability problem, which asks whether a given quantum state is separable. We investigate multipartite states of rank at most four which are PPT (i.e., all their partial…
The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful $k$-separability criteria of mixed $n$-partite ($n\geq 3$) quantum states to detect $k$-nonseparable $n$-partite quantum 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…
We present separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our…
We present a necessary and sufficient condition for the separability of multipartite quantum states, this criterion also tells us how to write a multipartite separable state as a convex sum of separable pure states. To work out this…
We consider the separability of various joint states of D-dimensional quantum systems, which we call "qudits." We derive two main results: (i) the separability condition for a two-qudit state that is a mixture of the maximally mixed state…
We derive criteria for $k$-separability of multipartite Quantum state
For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of separable (unentangled) matrices around the identity matrix. This implies a simple and…
We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient $k$-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems.…
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…
The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. This is a brief review in which we consider the problem for states in infinite dimensional Hilbert spaces.…
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…