Related papers: Largest separable balls around the maximally mixed…
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 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 introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
Suppose we have an unknown multipartite quantum state, how can we experimentally find out whether it is genuine multipartite entangled or not? Recall that even for a bipartite quantum state whose density matrix is known, it is already…
We explore classical to quantum transition of correlations by studying the quantum states located just outside of the classically-correlated-states-only neighborhood of the maximally mixed state (the largest separable ball (LSB)). We show…
Given a bipartite quantum system represented by a tensor product of two Hilbert spaces, we give an elementary argument showing that if either component space is infinite-dimensional, then the set of nonseparable density operators is…
According to usual definitions, entangled states cannot be given a separable decomposition in terms of products of local density operators. If we relax the requirement that the local density operators be positive, then an entangled quantum…
We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity…
We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our…
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 study the separability of bipartite quantum systems in arbitrary dimensions based on the Bloch representation of density matrices. We present two separability criteria for quantum states in terms of the matrices $T_{\alpha\beta}(\rho)$…
It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly…
Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we…
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…
A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respect to the natural measure is not entangled (is separable). We…
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…
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
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…
The geometric measure of entanglement of a pure quantum state is defined to be its distance to the space of product (seperable) states. Given an $n$-partite system composed of subsystems of dimensions $d_1,\ldots, d_n$, an upper bound for…
In this study, we investigate the problem of determining the maximum purity for absolutely separable and absolutely PPT quantum states. From the geometric viewpoint, this problem is equivalent to asking for the exact Euclidean radius of the…