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.

Highlights

  • Quantum Entanglement is a fundamental non-classical aspect of entities in the quantum realm, which disallows a reductionist description of a composite system in terms of the state and properties of its quantum constituents

  • The application of the Matryoshka GHZ-Bell states for n-qubit teleportation is reviewed and an extension of this formalism to more general classes of Matryoshka states is posited

  • An example of a state close to a perfect Matryoshka Q-GHZ state is given in the form of the genuinely entangled seven-qubit Xin-Wei Zha state

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Summary

Introduction

Quantum Entanglement is a fundamental non-classical aspect of entities in the quantum realm, which disallows a reductionist description of a composite system in terms of the state and properties of its quantum constituents. Bell showed that if one were to assume these principles, one obtains constraints in the form of certain inequalities, called Bell’s Inequalities, on the statistical correlations in the measured values of properties of the systems, and that the probabilities of the outcomes of a measurement performed on constituents of an entangled system violate the Bell inequality In this manner, it was shown that entanglement makes it impossible to simulate quantum correlations within the classical manner of thinking. Properties of spin squeezing when multi-qubit GHZ state and W state are superposed have been studied [33] These composite quantum states contain varying degrees of multilevel and genuine multipartite entanglement, which can be used for applications in quantum information processing [34, 35]. DGHZadk1,d1 ,ÆjGHZadk10,d1 ,ÆE 1⁄4 δkk0 ∀i (6) DBadki ,di ,ÆjBadki 0,di ,ÆE 1⁄4 δkk0 ∀i (7)

Matryoshka Q-GHZ states
Localised correlation generation: how can we generate entangled entanglement?
Generation of Matryoshka states using spin systems in condensed matter physics
D A k 1 j
Creating tesselated networks of Matryoshka states
Fractal network protocol
Surface codes, graph states and cluster states
Establishing multiparticle entanglement between nodes of a quantum communication network
Quantum networks, repeater protocols and quantum communication
Teleportation and superdense coding
Conclusion
Quantum Secret Sharing
Proposal 1
Proposal 2
Proposal 3
Linear teleportation scheme
Probabilistic circular teleportation scheme for arbitrary one-qubit states
Bidirectional teleportation of arbitrary two-qubit states
Quantum teleportation of arbitrary three-qubit state

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