Given a single copy of an unknown quantum state, it is impossible in principle to identify it. The mostly inaccessible information carried by the state is termed quantum information. In contrast to classical information, it cannot be copied or cloned. This concept provides a theoretical underpinning for all aspects of quantum communication and quantum computation. Here we use it to consider quantum teleportation.
Given a single copy of an unknown quantum state, it is impossible in principle to identify it. The mostly inaccessible information carried by the state is termed quantum information. In contrast to classical information, it cannot be copied or cloned. This concept provides a theoretical underpinning for all aspects of quantum communication and quantum computation. Here we use it to consider quantum teleportation.
This article considers the question of the teleportation protocol from an engineering perspective. The protocol ideally requires an authority that ensures that the two communicating parties have a perfectly entangled pair of particles available to them. But this cannot be unconditionally established to the satisfaction of the parties due to the fact that an unknown quantum state cannot be copied. This supports the view that quantum information cannot be treated on the same basis as classical information.
By quantum teleportation an unknown quantum state is destroyed at a sending place while its perfect replica state appears at a remote place via dual quantum and classical channels. Quantum teleportation allows for the transmission of quantum information to a distant location despite the impossibility of measuring or broadcasting the information to be transmitted. e classical teleportation is like a fax in which one could scan an object and send the information so that the object can be reconstructed at the destination. In this conventional facsimile transmission, the original object is scanned to extract partial information about it. e scanned information is then sent to the receiving station, where it is used to produce an approximate copy of the original object. e original object remains intact a er the scanning process. By contrast, in quantum teleportation, the uncertainty principle forbids any scanning process from extracting all the information in a quantum state. e nonlocal property of quantum mechanics enables the striking phenomenon of quantum teleportation. Bennett and coworkers28 showed that a quantum state can be teleported, provided one does not know that state, using a celebrated and paradoxical feature of quantum mechanics known as the Einstein-Podolsky-Rosen (EPR) e ect.11 ey found a way to scan out part of the information from an object A, which one wishes to teleport, while causing the remaining part of the information to pass to an object B, via the EPR e ect. In this process, two objects B and C form an entangled pair; object C is taken to the sending station, while object B is taken to the receiving station. At the sending station, object C is scanned together with the original object A, yielding some information and totally disrupting the state of A and C. e scanned information is sent to the receiving station, where it is used to select one of several treatments to be applied to object B, thereby putting B into an exact replica of the former state of A.
Due to the Heisemberg uncertainty principle, it is impossible to design a procedure which permits perfect cloning of an arbitrary, unknown "qubit" (the spin or polarization state of a single quantum system)1,2. However, it is believed that a perfect copying protocol can be achieved, at least in principle, if the qubit to be copied is destroyed in the original system. Quantum teleportation3,4 is supposed to allow for such a result. Here, this belief is shown to be invalidated by a fundamental uncertainty about the number of particles involved in any process, as predicted by Quantum Field Theory. As a result, teleportation cannot provide an infallible copying procedure for the single qubits, not even in the limit of perfect experimental sensitivities. The no-cloning theorem1,2 can then be generalized to the case of destroying the original. Teleportation remains an interesting statistical procedure, having an unavoidable theoretical error at the percent level or few orders of magnitude smaller, depending on the physical process that is used. Although it cannot be made arbitrarily small, such an error is small enough to remain hidden in present experiments.
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.
Bennett and his team pioneered the quantum teleportation protocol, a breakthrough where Alice transmits quantum information to Bob through a pre-shared entangled quantum channel. Remarkably, this transmission occurs without physically moving the information, relying on a combination of classical communication and quantum entanglement. This protocol not only demonstrates the essence of quantum entanglement but also underscores its potential in the realm of information transfer. The success of quantum teleportation experiments extends across various physical systems, with a particular emphasis on achieving effectiveness over long distances. Looking forward, future developments in this field may lead to multi-party protocols, thereby advancing both quantum communication and computing capabilities. A crucial component in quantum teleportation networks is controlled quantum teleportation (CQT), holding significant promise for the emerging concept of the quantum internet. In the preceding chapter, our exploration centered on the practical application of quantum teleportation protocols, with a specific focus on two key approaches: standard quantum teleportation and CQT. Our examination delved into the fundamental principles of quantum teleportation, encompassing critical concepts such as quantum entanglement, non-cloning, superposition, and the importance of measurements like fidelity. Throughout the chapter, we dedicated special attention to both the theoretical and experimental aspects of quantum teleportation, considering the intricacies of systems with continuous variables (CVs) as well as those with discrete variables (DVs).