Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations that are aimed at allowing us a better understanding of the physics involved in the process from different perspectives. With this purpose, here an approach based on graph theory is introduced and discussed in the context of some applications. Its main goal is to provide a fully symbolic framework for quantum teleportation from a dynamical viewpoint, which makes explicit at each stage of the process how entanglement and information swap among the qubits involved in it. In order to construct this dynamical perspective, it has been necessary to define some auxiliary elements, namely virtual nodes and edges, as well as an additional notation for nodes describing potential states (against nodes accounting for actual states). With these elements, not only the flow of the process can be followed step by step, but they also allow us to establish a direct correspondence between this graph-based approach and the usual state vector description. To show the suitability and versatility of this graph-based approach, several particular teleportation examples are examined in detail, which include bipartite, tripartite, and tetrapartite maximally entangled states as quantum channels. From the analysis of these cases, a general protocol is devised to describe the sharing of quantum information in presence of maximally entangled multi-qubit system.
Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations that are aimed at allowing us a better understanding of the physics involved in the process from different perspectives. With this purpose, here an approach based on graph theory is introduced and discussed in the context of some applications. Its main goal is to provide a fully symbolic framework for quantum teleportation from a dynamical viewpoint, which makes explicit at each stage of the process how entanglement and information swap among the qubits involved in it. In order to construct this dynamical perspective, it has been necessary to define some auxiliary elements, namely virtual nodes and edges, as well as an additional notation for nodes describing potential states (against nodes accounting for actual states). With these elements, not only the flow of the process can be followed step by step, but they also allow us to establish a direct correspondence between this graph-based approach and the usual state vector description. To show the suitability and versatility of this graph-based approach, several particular teleportation examples are examined in detail, which include bipartite, tripartite, and tetrapartite maximally entangled states as quantum channels. From the analysis of these cases, a general protocol is devised to describe the sharing of quantum information in presence of maximally entangled multi-qubit system.
Motivated by multi-particle entanglement, we propose a multi-party quantum parallel teleportation scheme in quantum wireless multi-hop networks (QWMNs) investigated with four-vertex graph-based entanglement. We show an ar- bitrary single-qubit quantum teleportation with graph state between directly connected two-party and an arbitrary two- qubit quantum teleportation based on four-vertex graph state followed by the multi-parity quantum teleportation based on four-vertex graph state where source node do not need share any entangled pairs with destination node but via intermediate nodes’ quantum swapping to finish the teleportation. Source node and intermediate nodes conduct von Neumann measurement and transmit their classical outcomes to the destination node independently in a parallel manner. Then destination node applies appropriate unitary operation to recover the source quantum state according to the received outcomes. This graph- based scheme extends the entanglement pattern in quantum teleportation, provides a perfect multi-party teleportation model. The proposed scheme improves the constructing flexibility of the network and reduces the communication delay, which has a wide application in quantum route selection.
Quantum Information Processing (QIP) exploits the principles of quantum mechanics to perform information storage, communication, and computation in ways that are fundamentally impossible within classical frameworks. This article presents a pedagogical overview of the mathematical foundations of quantum information theory, including qubits, Hilbert spaces, linear operators, quantum measurements, tensor products, density operators, and quantum entanglement. Building upon these concepts, we provide a detailed introduction to quantum teleportation, one of the most remarkable protocols in quantum communication. The discussion covers the no cloning theorem, the original teleportation protocol by Bennett et al., experimental realisations of quantum teleportation, and extensions involving probabilistic and multiqubit teleportation schemes. Particular emphasis is placed on the role of entanglement as a communication resource, together with the study of teleportation channels based on bipartite and multipartite quantum states. Various quantitative measures of entanglement, including concurrence, negativity, entanglement of formation, and relative entropy of entanglement, are reviewed alongside teleportation fidelity as a performance metric. Furthermore, the interplay between Bell nonlocality, mixed state entanglement, and teleportation efficiency is examined, followed by a survey of advanced developments such as controlled teleportation, bidirectional teleportation, cluster state teleportation, and recent advances in the Quantum 2.0 era. This review aims to provide students, researchers, and engineers with a coherent introduction to the theoretical foundations and practical significance of quantum teleportation in emerging quantum technologies.
This paper proposes a novel quantum networking protocol leveraging quantum teleportation for rapid quantum information transfer within a network. Traditional quantum network architectures suffer from limited transmission speeds due to the requirement of physically transporting qubits. This protocol overcomes this limitation by utilizing the quantum entanglement and Bell states to facilitate instantaneous information transfer, circumventing the need for direct qubit conveyance. The core of the protocol relies on establishing and maintaining entanglement between nodes, followed by a Bell state measurement and classical communication to reconstruct the quantum state at the destination. This design offers a significantly faster method for quantum information distribution compared to conventional approaches. The theoretical framework is presented with detailed mathematical formulations of the key steps, including the Bell state measurement, the process of quantum state transfer, and the necessary classical communication protocols. This work contributes to the advancement of quantum networking technology and provides a foundation for future high-speed quantum communication systems.
This work develops a process-based interpretation of quantum teleportation, quantum switching, and time, grounded in discrete process graphs rather than continuous space–time dynamics. We introduce a formal framework in which the fundamental unit of physical evolution is not the quantum state itself, but a discrete process step (process tact), represented as a unitary transformation acting on a structured process graph. Quantum teleportation is reinterpreted as a transition between isomorphic index layers of the same process graph, rather than as a transmission of a quantum state through space–time. In this framework, entanglement establishes a shared structural constraint, measurement performs index selection, and classical communication transfers index information only. The quantum state remains invariant under graph isomorphism, and teleportation is formalized as reindexation without a physical carrier. Time is shown to emerge as an ordering relation between process steps and index layers, not as a fundamental parameter. Changes in temporal ordering correspond to transitions between equivalent graph embeddings, enabling a natural interpretation of temporal displacement as index reassignment within a recursive process structure. Geometrically, these ideas are represented using recursive pentagon–pentagram embeddings, which serve as an exact structural analogy for quantum switching. The pentagram functions as a universal quantum switch, mediating transitions between distinct but isomorphic orderings. This construction provides an intuitive and mathematically consistent representation of indefinite causal order. The framework is directly connected to EPR correlations, quantum teleportation protocols, and the quantum switch, and is shown to be naturally compatible with the Everett (many-worlds) interpretation of quantum mechanics. Within this ontology, the wave function is treated as an objective process structure, and no collapse postulate is required. This work builds upon and extends previously published results on graph-based quantum key switching and emergent space–time structure, unifying them into a single process-theoretic description of quantum information transfer, causal order, and temporal indexing. Reference to previous foundational work: DOI 10.5281/zenodo.18498181. Reference to previous foundational work: DOI 10.5281/zenodo.18504244.
Very recently, we took part in a new development of quantum information, the so-called continuous variable (CV) quantum information theory. Such a further development is mainly due to the experimental and theoretical advantages offered by CV systems, i.e., quantum systems described by a set of observables, like position and momentum, which have a continuous spectrum of eigenvalues. According to this novel trend, quantum information protocols like quantum teleportation have been suitably extended to the CV framework. Here, we briefly review some mathematical tools relative to CV systems, and we consequently develop the concepts of quantum entanglement and teleportation in the CV framework by analogy with the qubit-based approach. Some connections between teleportation fidelity and entanglement properties of the underlying quantum channel are inspected. Next, we address the study of CV quantum teleportation networks where more users share a multipartite state and an arbitrary pair of them performs quantum teleportation. In this context, we show alternative protocols, and we investigate the optimal strategy that maximizes the performance of the network.
This book provides an in-depth exploration of the mathematical and theoretical foundations of quantum teleportation. Starting with the seminal 1993 work by C. H. Bennett and colleagues, this book delves into the intricate processes that enable the transfer of quantum information using non-local quantum entangled resources. It covers a broad spectrum of teleportation protocols for single and multi-qubit systems, explores the impact of quantum noise, and presents strategies to mitigate these effects. Overall features of this book are the following: • Detailed explanations of quantum mechanics concepts relevant to teleportation, such as qubits, entanglement, quantum evolution, noise, and measurement. • In-depth analysis of teleportation through noisy quantum channels, with models for amplitudedamping, bit-flip, phase-flip, and phase-damping noise. • Methods for minimizing the effects of noise, including weak and reversal measurements and environment- assisted techniques. • Case studies that illustrate the application of various teleportation protocols. • Comprehensive coverage of the necessary mathematics, including linear spaces, operators, tensor products, and partial trace operations. Primarily aimed at theoretical physicists, applied mathematicians, computer scientists, and engineers belonging to all branches of electrical technology, this book is both an introduction and a comprehensive guide to the field of quantum teleportation. It will also be beneficial to the interested scientientists and professionls belonging to physical chemistry, material science and information technology.