Quantum teleportation in higher dimension and entanglement distribution via quantum switches

Questioning of quantum information Guolin Wu The Center of Philosophy and Technology, School of Marxism South China University of Technology, Guangzhou, Guangdong, P. R. China. E-Mails: ssglwu@scut.edu.cn * The Center of Philosophy and Technology, School of Marxism. South China University of Technology, Guangzhou, Guangdong, P. R. China,510640; Tel.:0086-13660190516; Fax: 0086-2087114979 Accepted: 19 February 2015

Very recently we have witnessed a new development of quantum information, the so-called continuous variable (CV) quantum information theory. Such a further development has been 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 face 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.

Quantum teleportation plays an important role in quantum information science. In order to obtain the effect of quantum teleportation of a quantum state by using an entangled resource, the fidelity of teleporting the quantum state should be calculated. Braunstein and Kimble[Phys. Rev. Lett. 80 869 (1998)] derived a formula of calculating the fidelity of quantum teleportation for Gaussian entangled resource and any input state to be teleported. Then, the point is how to calculate the quantum teleportation fidelity for any entangled resource. In this paper, werealize this purpose by using the entangled state representation. First, we derive the Weyl expansion of any density operator by using the completeness relation between coherent state and P-representation. Then using the orthogonal property of entangled state representation and the traditional Kimble-Braunstein scheme of quantum teleportation, we further derive the mean density operator of the output state, which means that we establish the relation between the output density operator and the characteristic functions of the input state to be teleported and the entangled resources. The characteristic function of the output state is also derived which is in the concise form relating these two characteristic functions above. Then we further obtain a new formula for calculating the quantum teleportation fidelity for the coherent state input and any two-mode entangled resource. It is shown that the fidelity of teleportation can be easily calculated when the Q-function of the normally ordering form of entangled resource is known. This is a convenient way of obtaining the fidelity of teleportation. As its applications, some Gaussian and non-Gaussian entangled states are examined to teleport the coherent state, whose results are correct.

Advances in satellite quantum communications aim at reshaping the global telecommunication network by increasing the security of the transferred information. Here, we study the effects of atmospheric turbulence in continuous-variable entanglement distribution and quantum teleportation in the optical regime between a ground station and a satellite. More specifically, we study the degradation of entanglement due to various error sources in the distribution, namely, diffraction, atmospheric attenuation, turbulence, and detector inefficiency, in both downlink and uplink scenarios. As the fidelity of a quantum teleportation protocol using these distributed entangled resources is not sufficient, we include an intermediate station for either state generation, or beam refocusing, in order to reduce the effects of atmospheric turbulence and diffraction, respectively. The results show the feasibility of free-space entanglement distribution and quantum teleportation in downlink paths up to the LEO region, but also in uplink paths with the help of the intermediate station. Finally, we complete the study with microwave-optical comparison in bad weather situations, and with the study of horizontal paths in ground-to-ground and inter-satellite quantum communication.

Some general foundational issues of quantum mechanics are considered and are related to aspects of quantum computation. The importance of quantum entanglement and quantum information is discussed a...

Hyperentanglement, as a high-dimensional quantum entanglement phenomenon with multiple degrees of freedom, plays a critical role in quantum communication, quantum computing, and high-dimensional quantum state manipulation. Unlike entangled states in a single degree of freedom, hyperentangled states establish entanglement relationships simultaneously in multiple degrees of freedom, such as polarization, path, and orbital angular momentum. Through entanglement-based distribution techniques, high-dimensional quantum information networks can be constructed. On this basis, a fully connected quantum network with hyperentanglement is constructed in this work, and the polarization and time-bin degree-of-freedom hyperentanglement is realized through the process of second-harmonic generation and spontaneous parametric down-conversion in periodically poled lithium niobate (PPLN) waveguide cascades. The hyperentangled state is then multiplexed into a single-mode fiber by using dense wavelength division multiplexing (DWDM) technology for transmission to terminal users. The quality of the entangled states in the two degrees of freedom is characterized using Franson-type interference and photon-pair coincidence measurement techniques. Polarization entangled states are subjected to quantum state tomography, and entanglement distribution technology is employed to achieve long-distance distribution and quantum key transmission within the network. Experimental results show that the two-photon interference visibility of both polarization and time-bin entanglement is greater than 95%, demonstrating the high quality of the hyperentanglement in the network. After 100-km-entanglement distribution, the fidelity of the quantum states in both degrees of freedom remains above 88%, indicating the effectiveness of long-distance entanglement distribution in this network. Additionally, it is verified that this network supports the distribution of quantum keys over a distance of more than 50 km between users. These results confirm the feasibility of a fully connected quantum network with hyperentanglement and demonstrate the potential for constructing large-scale metropolitan networks by using hyperentanglement. As a higher-dimensional entanglement, hyperentangled states can significantly enhance the capacity and efficiency of quantum information processing. Although the quantum communication is still in its early stages of development, achieving stable storage and transmission of entangled states in large-scale metropolitan networks remains a great challenge. By utilizing the frequency conversion properties and high integration characteristics of the periodically poled lithium niobate waveguides, the three-user hyperentangled quantum network constructed in this work provides a new solution for developing the large-scale metropolitan networks with high-dimensional quantum information networks. It is expected to provide a new platform for quantum tasks such as superdense coding and quantum teleportation.

Quantum information with Gaussian states

Quantum entanglement is a peculiar phenomenon in quantum information science, characterized by nonclassical correlations between quantum states of subsystems in a quantum system. Since the proposal of the Einstein-Podolsky-Rosen (EPR) paradox by Einstein, Podolsky, and Rosen, quantum entanglement has sparked intense debates on local realism. Bells inequality experiment established the nonlocality of quantum mechanics. Currently, high-dimensional quantum entanglement of both deterministic and random states can be realized in systems such as photons and cold atoms. Technologies such as quantum teleportation, quantum teleportation, quantum computing, and others rely on quantum entanglement to achieve effects beyond classical limitations. Current research focuses on the implementation of macroscopic quantum entanglement and its significance in fundamental problems of quantum mechanics. Quantum entanglement opens up a new paradigm for information processing with broad application prospects. It is necessary to conduct in-depth research on the nature of quantum entanglement and its advantages in information processing. This paper reviews the theoretical foundations of quantum entanglement, methods of generation and detection, and research progress in its applications in the field of quantum information. It discusses the important applications of quantum entanglement in quantum communication, computing, and sensing and provides an outlook on the future development prospects of quantum entanglement technologies.

Faithful long-distance quantum teleportation necessitates prior entanglement distribution between two communicated locations. The particle carrying on the unknown quantum information is then combined with one particle of the entangled states for Bell-state measurements, which leads to a transfer of the original quantum information onto the other particle of the entangled states. However in most of the implemented teleportation experiments nowadays, the Bell-state measurements are performed even before successful distribution of entanglement. This leads to an instant collapse of the quantum state for the transmitted particle, which is actually a single-particle transmission thereafter. Thus the true distance for quantum teleportation is, in fact, only in a level of meters. In the present experiment we design a novel scheme which has overcome this limit by utilizing fiber as quantum memory. A complete quantum teleportation is achieved upon successful entanglement distribution over 967 meters in public free space. Active feed-forward control techniques are developed for real-time transfer of quantum information. The overall experimental fidelities for teleported states are better than 89.6%, which signify high-quality teleportation.

Abstract: This book, Quantum Networks and Secure Communication, presents a comprehensive and interdisciplinary investigation into the foundations, architectures, protocols, and security mechanisms underpinning quantum communication networks. Rooted in the principles of quantum mechanics—entanglement, superposition, and the no-cloning theorem—the text develops a conceptual framework that redefines secure data transmission by exploring how quantum states can be reliably distributed across spatially separated nodes. The work begins by establishing theoretical constructs including quantum bits (qubits), quantum teleportation, and entanglement distribution, and proceeds to analyze practical implementations of Quantum Key Distribution (QKD) through discrete-variable and continuous-variable protocols. The methodological approach combines analytical modeling, system simulation, and empirical evaluations of existing global deployments such as China’s Micius satellite, Europe’s OpenQKD, and the U.S. Quantum Internet Blueprint. By integrating cryptographic theory with quantum physics and network engineering, the book identifies key vulnerabilities—including photon number splitting and quantum hacking—and examines countermeasures such as decoy-state methods and device-independent QKD. Key findings emphasize the superiority of quantum-based security over classical cryptography in adversarial environments and underscore the implementation challenges of scalability, synchronization, and interoperability. The book concludes by mapping out future directions toward a fully realized quantum internet, offering regulatory, ethical, and governance perspectives. This work serves as a critical resource for advancing the understanding and application of quantum-secure networks in both academic and policy-making arenas. Keywords Quantum networks, quantum communication, quantum key distribution, entanglement, no-cloning theorem, secure communication, QKD protocols, device-independent QKD, photon number splitting, quantum hacking, quantum internet, quantum cryptography, network architecture, quantum repeaters, quantum interoperability, quantum memory, integrated photonics, post-quantum security, quantum authentication, entanglement distribution, quantum network deployment.

Quantum teleportation is the fundamental communication unit in quantum communication. Here, a three-level system is selected for storing and transmitting quantum information, due to its unique advantages, such as lower cost than a higher-level system and higher capacity and security than a two-level system. It is known that the key procedure for perfect teleportation is the distribution of entanglement through quantum channel. However, amounts of noise existing in the quantum channel may interfere the entangled state, causing the degradation of quantum entanglement. In the physical implementations of quantum communication schemes, noise acting on the carriers of successive transmissions often exhibits some correlations, which is the so called quantum memory channel. In this paper, a memory channel model during the entanglement distribution phase is constructed and the uniform expression of the evolution of a two-qutrit entangled state under different kinds of correlated noise is derived. Finally, Pauli noise and amplitude damping noise as the typical noise source are considered to analyze the influence of memory effects of noise on qutrit teleportation. It is expected to show that three-level teleportation under these two types of channels can generally enhance the robustness to noise if the Markovian correlations of quantum channel are taken into consideration.

The architecture proposed by Duan, Lukin, Cirac, and Zoller (DLCZ) for long-distance quantum communication with atomic ensembles is analyzed. Its fidelity and throughput in entanglement distribution, entanglement swapping, and quantum teleportation is derived within a framework that accounts for multiple excitations in the ensembles as well as loss and asymmetries in the channel. The DLCZ performance metrics that are obtained are compared to the corresponding results for the trapped-atom quantum communication architecture that has been proposed by a team from the Massachusetts Institute of Technology and Northwestern University (MIT/NU). Both systems are found to be capable of high-fidelity entanglement distribution. However, the DLCZ scheme only provides conditional teleportation and repeater operation, whereas the MIT/NU architecture affords full Bell-state measurements on its trapped atoms. Moreover, it is shown that achieving unity conditional fidelity in DLCZ teleportation and repeater operation requires ideal photon-number resolving detectors. The maximum conditional fidelities for DLCZ teleportation and repeater operation that can be realized with non-resolving detectors are 1/2 and 2/3, respectively.

Quantum teleportation is one of the most basic quantum protocols, which transfers an unknown quantum state from one location to another through local operation and classical communication by using shared quantum entanglement without physical transfer of the information carrier. And it has been widely used in various quantum information protocols such as entanglement swapping, quantum repeaters, quantum gate teleportation, quantum computation based on measurement, and quantum teleportation networks, which have important application value in quantum computation and quantum information. Quantum teleportation is a naturally bipartite process, in which an unknown quantum state can only be transmitted from one node to another. With the further development of quantum information research, it is necessary to transfer quantum states or quantum information among more and more nodes. Multipartite quantum protocols are expected to form fundamental components for larger-scale quantum communication and computation. A bipartite quantum teleportation should be extended to a multipartite protocol known as a quantum teleportation network. In this paper, a multifunctional quantum teleportation network is proposed theoretically. We first propose a special method of constructing four-partite quantum resources in continuous variables (CVs), and based on this, construct two different types of CV quantum teleportation networks. One type of network contains just one quantum teleportation process consisting of a sender, a receiver and two controllers. In this type of network, the unknown quantum state can be recovered at any other node according to the requirement after the measurement in the input node, which enriches the transfer direction and transfer mode of the unknown quantum state. And meanwhile, the two controllers can control the transfer of a quantum state from the sender to the receiver by restricting the sender and receiver’s access to their information, which makes the quantum teleportation network controllable. The other type of network has two quantum teleportation processes, each containing only a sender, a receiver and no controllers, which increases the number of quantum states that can be transmitted. Then we analyze the dependence of the fidelity of each quantum teleportation network on different physical parameters, and compare the characteristics, advantages and disadvantages among different types of quantum teleportation networks. The scheme for constructing a multifunctional quantum teleportation network in this paper shows some advantages, such as the greater number of quantum nodes, diversity of types, simple operation procedure. And all these advantages provide a broader application prospect for establishing larger and more complex quantum information networks in the future and quicken the pace of the application of quantum information.

In this presentation, an overview of Quantum Information Systems is given. Therefore, the postulates of quantum mechanic are given based on one interpretation that is called the Copenhagen interpretation. The main pillars of quantum mechanics are: Superposition, Interference, and Entanglement. Quantum Information Systems comprise three disciplines: Quantum Computation, Quantum Communication, and Quantum Control. Each one of them has a number of topics with some implementations that have reached the commercial level. Quantum Computation has three models: the circuit model that is using different techniques like superconducting elements and special Silicon-based elements. The Adiabatic quantum model has reached the commercial stage through a startup company using superconducting chips. The categorical quantum model is based on category theory and one of its main applications is the study and verification of network and cryptographic protocols. Quantum communication started with defining the basic unit of information, the qubit. Then the quantum compression theorem was proved. The quantum channel capacity problem was divided into two problems: transmitting classical information over a quantum channel, and transmitting quantum information over a quantum channel. The first problem was partially resolved. However, the second problem is being researched upon. Two applications will be briefly presented: quantum teleportation and superdense coding. Both of them employs quantum entanglement. Quantum Key Distribution (QKD) using cryptographic protocols has received much attention due to its importance in network security. A number of protocols have been proposed and some of them have been implemented, and now a number of commercial products have been announced. Also, some experimental networks have been implemented. QKD using space links have been proposed and experimented with. In few years quantum satellites will be launched. Quantum cryptographic protocols are being proposed to protect infrastructure networks like the electric power grid. Also, it is being used as a countermeasure against global spying networks like ECHELON that are detrimental for national economies. The Quantum Internet is also being considered using quantum teleportation together with Cavity Quantum Electrodynamics with some experimental work going on. Quantum Control is essential for both Quantum Computation and Quantum Communication. Intensive research is going on in: State estimation (called Quantum State Tomography), and system identification (called Process State Tomography), and Quantum Feedback Control. The basic concepts will be briefly considered in this presentation. University education has witnessed major changes to support the above developments. At the postgraduate level many universities offer many courses related to the above disciplines. Recently, a number of institutions started to offer undergraduate courses and some of them have even started to introduce Quantum Engineering 4 year undergraduate programs. A brief account will be given to such developments.

In this presentation, an overview of Quantum Information Systems is given. Therefore, the postulates of quantum mechanics are given based on one interpretation that is called the Copenhagen interpretation. The main pillars of quantum mechanics are: Superposition, Interference, and Entanglement. Quantum Information Systems comprise three disciplines: Quantum Computation, Quantum Communication, and Quantum Control. Each one of them has a number of topics with some implementations that have reached the commercial level. Quantum Computation has three models: the circuit model that is using different techniques like superconducting elements and special Silicon-based elements. The Adiabatic quantum model has reached the commercial stage through a start-up company using superconducting chips. The categorical quantum model is based on category theory and one of its main applications is the study and verification of network and cryptographic protocols. Quantum communication started with defining the basic unit of information, the qubit. Then the quantum compression theorem was proved. The quantum channel capacity problem was divided into two problems: transmitting classical information over a quantum channel, and transmitting quantum information over a quantum channel. The first problem was partially resolved. However, the second problem is being researched upon. Two applications will be briefly presented: quantum teleportation and superdense coding. Both of them employs quantum entanglement. Quantum Key Distribution (QKD) using cryptographic protocols has received much attention due its importance in network security. A number of protocols have been proposed and some of them have been implemented, and now a number of commercial products have been announced. Also, some experimental networks have been implemented. QKD using space links have been proposed and experimented with. In few years quantum satellites will be launched. Quantum cryptographic protocols are being proposed to protect infrastructure networks like the electric power grid. Also, it is being used as a countermeasure against global spying networks like ECHELON that are detrimental for national economies. The Quantum Internet is also being considered using quantum teleportation together with Cavity Quantum Electrodynamics with some experimental work going on. Quantum Control is essential for both Quantum Computation and Quantum Communication. Intensive research is going on in: State estimation (called Quantum State Tomography), system identification (called Quantum Process Tomography), and Quantum Feedback Control. The basic concepts will be briefly considered in this presentation. University education has witnessed major changes to support the above developments. At the postgraduate level many universities offer many courses related to the above disciplines. Recently, a number of institutions started to offer undergraduate courses and some of them have even started to introduce Quantum Engineering 4 years undergraduate programs. A brief account will be given to such developments.