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Quantum Teleportation: An Operator Algebraic Perspective

Alexandre Conlon

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We show that quantum teleportation is intimately connected to Jones' basic construction. This connection leads to generalized, or hybrid teleportation protocols to simultaneously transmit classical and quantum information through finite dimensional von Neumann algebras. We present two operationally concrete teleportation protocols, Hybrid teleportation and our so-called Scaffolding teleportation. Under some mild symmetry assumptions, we establish that any teleportation scheme in the scaffolding framework is equivalent to a teleportation scheme of a special form.

DOI
10.22215/etd/2022-14894

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We show that quantum teleportation is intimately connected to Jones' basic construction. This connection leads to generalized, or hybrid teleportation protocols to simultaneously transmit classical and quantum information through finite dimensional von Neumann algebras. We present two operationally concrete teleportation protocols, Hybrid teleportation and our so-called Scaffolding teleportation. Under some mild symmetry assumptions, we establish that any teleportation scheme in the scaffolding framework is equivalent to a teleportation scheme of a special form.
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Abstract Chapter 14 discusses the quantum communication protocol called quantum teleportation, which uses the quantum correlations in an entangled particle pair shared between two observers to transmit the information stored in the (unknown) quantum state of a target system from one of the observers to the other. After reviewing the theoretical basics we showcase some of the important experimental demonstrations of teleportation. We then turn to more general protocols related to teleportation such as entanglement swapping, and the general formalism of isometries, before inspecting the option of delayed-choice entanglement swapping. In the light of these findings we compare teleportation to classical information transfer and inspect the related dense-coding protocol. Finally, we give an overview of basic quantum key distribution protocols is given, including the Bennett-Brassard-84 protocol based on conjugate coding and the entanglement-based Ekert-91 protocol
With the advent of quantum technology, the exploration of quantum teleportation has become increasingly important, and it has provided a glimpse of the potential of quantum information science. The current research delves into the background of quantum teleportation, emphasizing its key role in advancing quantum communication and computation. Implications of this research are that it has the potential to revolutionize data transmission and processing, providing a secure and efficient means of exchanging quantum information. This paper is structured to provide a comprehensive study of quantum teleportation, starting with a literature review that lays the foundation for our work. Afterward, the details of our research are presented, including the theoretical framework and the proposed methodology for realizing the quantum teleportation protocol. We provide a careful overview of the technical details, demonstrating the complexity of quantum state preparation, entanglement distribution, and Bell state measurements. Our empirical section demonstrates the practical application of these protocols, providing empirical evidence of successful teleportation of quantum states. The theoretical predictions are confirmed by the experimental results, which validate the feasibility and reliability of our approach. Conclusions drawn from the experiments emphasize the robustness of quantum teleportation as a viable technology for future quantum networks.
A bstract We present an operator algebraic perspective on the black hole information problem. For a black hole after Page time that is entangled with the early radiation we formulate a version of the information puzzle that is well-posed in the G → 0 limit. We then give a description of the information recovery protocol in terms of von Neumann algebras using elements of the Jones index theory of type II 1 subfactors. The subsequent evaporation and recovery steps are represented by Jones’s basic construction, and an operation called the canonical shift. A central element in our description is the Jones projection, which leads to an entanglement swap and implements an operator algebraic version of a quantum teleportation protocol. These aspects are further elaborated on in a microscopic model based on type I algebras. Finally, we argue that in the emergent type III algebra the canonical shift may be interpreted as a spacetime translation and, hence, that at the microscopic level “translation = teleportation”.
A simplification scheme of probabilistic teleportation of two-particle state of general form is given. By means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neumann measurement and classically controlled operations, we construct an efficient quantum logical network for implementing the new scheme of probabilistic teleportation of a two-particle state of general form. PACS: 03.65.Bz, 03.67.Hk Quantum teleportation is one of the most striking progress of quantum information theory. 1 2,3 It will be useful in quantum computers. It can be used to transmit information reliably in noisy situations where a message would otherwise be degraded, and to transfer information from fleeting or hard-to-control carriers to particles more suitably for permanent storage. Moreover, it may have application in quantum cryptography and quantum dense coding. 4−8 In 1993, Bennett et al presented the theory of quantum teleportation which allows the transmission of an unknown qubit state from a sender ”Alice ” to a spatially distant receiver ”Bob” via a quantum channel with the aid of some classical communication. 1 Teleportation has drawn