Related papers: A note on separability criteria for multipartite s…
A geometric understanding of entanglement is proposed based on local measurements. Taking recourse to the general structure of density matrices in the framework of Euclidean geometry, we first illustrate our approach for bipartite Werner…
We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…
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 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 investigate the separability of arbitrary dimensional tripartite sys- tems. By introducing a new operator related to transformations on the subsystems a necessary condition for the separability of tripartite systems is presented.
The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric…
We provide necessary and sufficient conditions for the partial transposition of bipartite harmonic quantum states to be nonnegative. The conditions are formulated as an infinite series of inequalities for the moments of the state under…
In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudo-spin observables for an arbitrary non-positive Hermitian…
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…
A quantum system consisting of two subsystems is separable if its density matrix can be written as $\rho=\sum_A w_A\,\rho_A'\otimes\rho_A''$, where $\rho_A'$ and $\rho_A''$ are density matrices for the two subsytems. In this Letter, it is…
We consider the implications of the Revised Symmetrization Postulate (see quant-ph/9908078) for states of more than two particles. We show how to create permutation symmetric state vectors and how to derive alternative state vectors that…
We derive a hierarchy of separability criteria for multi-mode continuous variable systems. They permit to study in a unified way the k-partite entanglement of broad classes of Gaussian and non- Gaussian states. With specific examples we…
We consider the concept of "the permutationally invariant (PI) part of a density matrix," which has proven very useful for both efficient quantum state estimation and entanglement characterization of $N$-qubit systems. We show here that the…
We study entanglement in mixed bipartite quantum states which are invariant under simultaneous SU(2) transformations in both subsystems. Previous results on the behavior of such states under partial transposition are substantially extended.…
The positive partial transpose test is one of the main criteria for detecting entanglement, and the set of states with positive partial transpose is considered as an approximation of the set of separable states. However, we do not know to…
We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…
We derive a many-particle inseparability criterion for mixed states using the relation between single-mode and many-particle nonclassicalities. It works very well not only in the vicinity of the Dicke states, but also for the superposition…
Inseparability criteria for continuous and discrete bipartite quantum states based on moments of annihilation and creation operators are studied by developing the idea of Shchukin-Vogel criterion [Phys. Rev. Lett. {\bf 95}, 230502 (2005)].…
We introduce an operational procedure to determine, with arbitrary probability and accuracy, optimal entanglement witness for every multipartite entangled state. This method provides an operational criterion for separability which is…
Production and verification of multipartite quantum state are an essential step in quantum information processing. In this work, we propose an efficient method to decompose symmetric multipartite observables, which are invariant under…