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Generation and Application of Nested Entanglement in Matryoshka Quantum Resource-States

Mrittunjoy Guha Majumdar

Published Jul 10, 2020• 1 citation
Publisher

Abstract

Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. Nested entanglement provides resource-states for quantum information processing. In this paper, Matryoshka quantum resource-states, which contain nested entanglement patterns, has been studied. A novel scheme for the generation of such quantum states has been proposed using an anisotropic XY spin-spin interaction-based model. The application of the Matryoshka GHZ-Bell states for n-qubit teleportation is reviewed and an extension to more general Matryoshka ExhS-Bell states is posited. An example of Matryoshka ExhS-Bell states is given in the form of the genuinely entangled seven-qubit Xin-Wei Zha state. Generation, characterisation and application of this seven-qubit resource state in theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation are presented.

DOI
10.20944/preprints202007.0199.v1

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Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. Nested entanglement provides resource-states for quantum information processing. In this paper, Matryoshka quantum resource-states, which contain nested entanglement patterns, has been studied. A novel scheme for the generation of such quantum states has been proposed using an anisotropic XY spin-spin interaction-based model. The application of the Matryoshka GHZ-Bell states for n-qubit teleportation is reviewed and an extension to more general Matryoshka ExhS-Bell states is posited. An example of Matryoshka ExhS-Bell states is given in the form of the genuinely entangled seven-qubit Xin-Wei Zha state. Generation, characterisation and application of this seven-qubit resource state in theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation are presented.
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.
Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. In this paper, generation, characterisation and application of a genuine genuinely entangled seven-qubit resource state is studied. Theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation as well as three schemes for undertaking tripartite quantum state sharing are presented.
Since the first protocol of quantum teleportation based on an EPR pair was presented by Bennett et al. in 1993, it has become a hot topic in quantum communication. It is known that entanglement plays a key role in quantum teleportation. Various schemes of controlled quantum teleportation and bidirectional controlled quantum teleportation have been developed by using all kinds of multi-parties entangled states as a quantum channel, e.g. GHZ states, W states, 5-qubit cluster states, 6-qubit cluster states, 7-qubit cluster states, maximally entangled 5-qubit states, maximally entangled 6-qubit states, genuine entangled 6-qubit states, genuine entangled 7-qubit states, genuine entangled 8-qubit states. In this paper, a genuine entangled 9-qubit state is used as channel of quantum teleportation, and two schemes of bidirectional controlled quantum teleportation are proposed. One scheme is that with the control of Charlie Alice can transmit an arbitrary unknown qubit state to Bob and Bob can transmit an arbitrary unknown 3-qubit state to Alice in the same time. Another scheme is that with the control of Charlie Alice and Bob can transmit an arbitrary unknown 2-qubit to each other simultaneously. Compared with the existed schemes, our scheme can transmit more qubits of arbitrary state in total by an entangled state, and the intrinsic efficiency of our scheme is maybe the best. Moreover, the genuine entangled 9-qubit state used in our scheme can be produced through some simple quantum unitary gates.
This dissertation consists of three sections. In the first section, we discuss the generation \nof arbitrary two-qubit entangled states and present three generation methods. \nThe first method is based on the interaction of an atom with classical and quantized \ncavity fields. The second method is based on the interaction of two coupled two-level \natoms with a laser field. In the last method, we use two spin-1/2 systems which \ninteract with a tuned radio frequency pulse. Using those methods we have generated \ntwo qubit arbitrary entangled states which is widely used in quantum computing and \nquantum information. In the second section, we discuss a possible experimental implementation \nof quantum walk which is based on the passage of an atom through a \nhigh-Q cavity. The chirality is determined by the atomic states and the displacement \nis characterized by the photon number inside the cavity. Our scheme makes quantum \nwalk possible in a cavity QED system and the results could be widely used on \nquantum computer. In the last section, we investigate the properties of teleporting \nan arbitrary superposition of entangled Dicke states of any number of atoms (qubits) \nbetween two distant cavities. We also studied teleporting continuous variables of an \noptical field. Teleportation of Dicke states relies on adiabatic passage using multiatom \ndark states in each cavity and a conditional detection of photons leaking out of both cavities. In the continuous variables teleportation scheme we first reformulate \nthe protocol of quantum teleportation of arbitrary input optical field states in \nthe density matrix form, and established the relation between the P-function of the \ninput and output states. We then present a condition involving squeeze parameter \nand detection efficiency under which the P-function of the output state becomes the \nQ function of the input state such that any nonclassical features in the input state \nwill be eliminated in the teleported state. Based on the research in this section we \nhave made it possible of arbitrary atomic Dicke states teleportation from one cavity \nto another, and this teleortation will play an essential role in quantum communication. \nSince quantum properties is so important in quantum communication, the \ncondition we give in this section to distinguish classical and quantum teleportation is \nalso important.
Abstract Based on a seven-qubit entangled state, Chen et al (2020 Int. J. Theor. Phys. 59 1402) presented a scheme for controlled quantum teleportation. Using the same quantum channel state, we put forward a new scheme in which the quantum information sender can also transmit a Bell state to receiver under the agreement and assist of the controller. The comparison with Chen et al’s scheme is made and reveals its distinct advantage of reducing the classical resource consumption and increasing the intrinsic efficiency as well as degrading the complexity of necessary operations.