**Abstract**

In this chapter, nested multilevel entanglement is formulated and discussed in terms of *Matryoshka* states. The generation of such states that contain nested patterns of entanglement, based on an anisotropic XY model has been proposed. Two classes of multilevel-entanglement- the *Matryoshka Q-GHZ states* and *Matryoshka generalised GHZ states*, are studied. Potential applications of such resource states, such as for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation are proposed and discussed, in terms of a Matryoshka state over seven qubits. We also discuss fractal network protocols, surface codes and graph states as well as generation of arbitrary entangled states at remote locations in this chapter.

**Keywords:** Quantum Computation, Multipartite Entanglement, Quantum State Sharing
