Three distant labs A, B and C, having no prior entanglement can establish a shared GHZ state, when one of them say A sends two particles to B and C for their local actions. The mediating particles remain separable from each other and from the particl
es of A, B and C. We prove that in this way, GHZ states are shared with a probability $frac{1}{7}$. We also show how separable particles can be mediated to establish arbitrary $d-$ dimensional Bell states between distant labs. Our method is constructive and allows generaization of GHZ sharing between any number of parties and in any dimension. The proposed method may facilitate the construction of multi-node quantum networks and many other processes which use multi-partite entangled states.
Quantum protocols for secret sharing usually rely on multi-party entanglement which with present technology is very difficult to achieve. Recently it has been shown that sequential manipulation and communication of a single $d-$ level state can do th
e same task of secret sharing between $N$ parties, hence alleviating the need for entanglement. However the suggested protocol which is based on using mutually unbiased bases, works only when $d$ is a prime number. We propose a new sequential protocol which is valid for any $d$.
We study the Kitaev-Ising model, where ferromagnetic Ising interactions are added to the Kitaev model on a lattice. This model has two phases which are characterized by topological and ferromagnetic order. Transitions between these two kinds of order
are then studied on a quasi-one dimensional system, a ladder, and on a two dimensional periodic lattice, a torus. By exactly mapping the quasi-one dimensional case to an anisotropic XY chain we show that the transition occurs at zero $lambda$ where $lambda$ is the strength of the ferromagnetic coupling. In the two dimensional case the model is mapped to a 2D Ising model in transverse field, where it shows a transition at finite value of $lambda$. A mean field treatment reveals the qualitative character of the transition and an approximate value for the transition point. Furthermore with perturbative calculation, we show that expectation value of Wilson loops behave as expected in the topological and ferromagnetic phases.
