Non-local properties of symmetric two-qubit states are quantified in terms of a complete set of entanglement invariants. We prove that negative values of some of the invariants are signatures of quantum entanglement. This leads us to identify sufficient conditions for non-separability in terms of entanglement invariants. Non-local properties of two-qubit states extracted from (i) Dicke state (ii) state generated by one-axis twisting Hamiltonian, and (iii) one-dimensional Ising chain with nearest neighbour interaction are analyzed in terms of the invariants characterizing them.

Production and analysis of non-Gaussian radiation fields has evinced a lot of attention recently. Simplest way of generating such non-Gaussians is through adding (subtracting) photons to Gaussian fields. Interestingly, when photons are added to classical Gaussian fields, the resulting states exhibit non-classicality. Two important classical Gaussian radiation fields are coherent and thermal states. Here, we study the non-classical features of such states when photons are added to them. Nonclassicality of these states shows up in the negativity of the Wigner function. We also work out the entanglement potential, a recently proposed measure of non-classicality for these states. Our analysis reveals that photon added coherent states are non-classical for all seed beam intensities; their non-classicality increases with the addition of more number of photons. Thermal state exhibits non-classicality at all temperatures, when a photon is added; lower the temperature, higher is their non-classicality.

We derive necessary and sufficient inseparability conditions imposed on the variance matrix of symmetric qubits. These constraints are identified by examining a structural parallelism between continuous variable states and two-qubit states. Pairwise entangled symmetric multiqubit states are shown here to obey these constraints. We also bring out an elegant local invariant structure exhibited by our constraints. © 2006 Elsevier B.V. All rights reserved. Entanglement is a central property of multipartite quantum systems as it forms the corner stone of all aspects of quantum information, communication, and computation [1]. The first task is to find a criterion if a given state is entangled or not. Peres-Horodecki inseparability criterion [2] viz., positivity under partial transpose (PPT) has been extremely fruitful in addressing this question and provides necessary and sufficient conditions for (2 × 2)-and (2 × 3)-dimensional systems. It is found that the PPT criterion is significant in the case of infinite-dimensional bipartite continuous variable (CV) states too. An important advance came about through an identification of how Peres-Horodecki criterion gets translated elegantly into the properties of the second moments (uncertainties) of CV states [3]. This results in restrictions [3,4] on the covariance matrix of an entangled bipartite CV state. In the special case of two-mode Gaussian states, where the basic entanglement properties are imbibed in the structure of its covariance matrix, the restrictions on the covariance matrix are found [3,4] to be necessary and sufficient for inseparability. Investigations on the structure of variance matrix have proved to be crucial in understanding the issue of entanglement in CV states [5][6][7] and * Corresponding author.E-mail address: arutth@rediffmail.com (A.R. Usha Devi).a great deal of interest has been catching up in experimentally accessible, simple conditions of inseparability involving higher order moments [8][9][10]. In a parallel direction, growing importance is being evinced towards quantum correlated macroscopic atomic ensembles [11][12][13][14][15]. In the last few years experimental generation of entangled multiqubit states in trapped-ion systems [16][17][18][19], where individual particles can be manipulated, has been accomplished, giving new hopes for scalable quantum information processing.In the present Letter, we explore a structural parallelism in CV states and two-qubit systems by constructing covariance matrix of the latter. We show that pairwise entanglement between any two-qubits of a symmetric N -qubit state is completely characterized by the off-diagonal block of the two-qubit covariance matrix. We establish the inseparability constraints satisfied by the covariance matrix and these are identified to be equivalent to the generalized spin squeezing inequalities [20] for two-qubit entanglement. The interplay between two basic principles viz., the uncertainty principle and the nonseparability gets highlighted through the restriction on the ...

Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a classification scheme for pairwise entanglement is proposed. The invariant criteria given here are shown to be related to the recently proposed (Phys. Rev. Lett. 95, 120502 (2005)) generalized spin squeezing inequalities for pairwise entanglement in symmetric multi-qubit states.