相关论文: Separability Criterion for Density Matrices
We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…
We study families of positive and completely positive maps acting on a bipartite system $\mathbb{C}^M\otimes \mathbb{C}^N$ (with $M\leq N$). The maps have a property that when applied to any state (of a given entanglement class) they result…
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.…
The separability problem is formulated in terms of a characterization of a single entanglement witness. More specifically, we show that any (in general multipartite) state \varrho is separable if and only if a specially constructed…
We present a necessary and sufficient condition for three qutrit density matrices to be the one-particle reduced density matrices of a pure three-qutrit quantum state. The condition consists of seven classes of inequalities satisfied by the…
We investigate separability and entanglement of mixed states in ${\cal C}^2\otimes{\cal C}^2\otimes{\cal C}^N$ three party quantum systems. We show that all states with positive partial transposes that have rank $\le N$ are separable. For…
We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow to detect the entanglement…
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of…
This paper characterizes two forms of separability of pure states of systems of n qubits: (i) into a tensor product of n qubit states, and (ii), into a tensor product of 2 subsystems states of p and q qubits respectively with p+q=n. For…
The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices,…
Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of…
We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover, it…
We analyze and compare the mathematical formulations of the criterion for separability for bipartite density matrices and the Bell inequalities. We show that a violation of a Bell inequality can formally be expressed as a witness for…
We use the generalized concurrence approach to investigate the general multipartite separability problem. By extending the preconcurrence matrix formalism to arbitrary multipartite systems, we show that the separability problem can be…
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 present the necessary and sufficient conditions of separability for multipartite pure states. These conditions are very simple, and they don't require Schmidt decomposition or tracing out operations. We also give a…
We present a method to derive separability criteria for the different classes of multiparticle entanglement, especially genuine multiparticle entanglement. The resulting criteria are necessary and sufficient for certain families of states.…
A new quantum mechanical notion -- Conditional Density Matrix -- is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of…
For a quantum state in a bipartite system represented as a density matrix, researchers used the realignment matrix and functions on its singular values to study the separability of the quantum state. We obtain bounds for elementary…
Explicit separability of general two qubits density matrices is related to Lorentz transformations. We use the 4-dimensional form R(u,v=0,1,2,3) of the Hilbert-Schmidt (HS) decomposition of the density matrix. For the generic case in which…