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.
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.
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, referred to as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, referred to as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the advantages of the two encodings have emerged [1] . In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete- and continuous-variable quantum states [2] , [3] , located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Following the first protocols based on this resource, such as the remote preparation of continuous-variable qubits [4] , or a violation of an Einstein-Podolsky-Rosen steering inequality [5] , we will here report our latest experimental results on entanglement swapping and quantum teleportation protocols using hybrid entangled states based on different encodings [6] .
Hybrid entanglement between discrete-variable (DV) and continuous-variable (CV) quantum systems is an essential resource for heterogeneous quantum networks. Our previous work showed that in lossy channels the teleportation of DV qubits, via CV-entangled states, can be significantly improved by a new protocol defined by a modified Bell state measurement at the sender. This work explores whether a new, similarly modified, CV-based teleportation protocol can lead to improvement in the transfer of hybrid entangled states. To set the scene, we first determine the performance of such a modified protocol in teleporting CV-only qubits, showing that significant improvement over traditional CV-based teleportation is obtained. We then explore similar modifications in the teleportation of a specific hybrid entangled state showing that significant improvement over traditional CV-based teleportation is again found. For a given channel loss, we find teleporting the DV qubit of the hybrid entangled state can always achieve higher fidelity than teleporting the CV qubit. We then explore the use of various non-Gaussian operations in our modified teleportation protocol, finding that, at a cost of lower success probability, quantum scissors provides the most improvement in the loss tolerance. Our new results emphasize that in lossy conditions, the quantum measurements undertaken at the sender can have a surprising and dramatic impact on CV-based teleportation.
Summary form only given. Traditionally quantum information research has centred on discrete quantum variables, particularly binary variables (qubits). However, recently much attention has focused on quantum information manipulations with continuous variables such as the amplitude and phase of the electromagnetic field. As well as offering the possibility of high data rates, continuous variables also exhibit greater versatility in realizing certain operations. For example teleportation, in which quantum information is passed intact through a classical channel with the assistance of shared entanglement, can be achieved more efficiently using continuous variable techniques. I review recent work on the characterization of teleportation and entanglement swapping and present new work on interferometric tests of teleportation. These interferometric tests are important because they allow the efficacy of teleportation to be checked without knowledge of the input quantum state. They can be applied equally to the cases of discrete and continuous variable inputs and in so doing highlight unexpected similarities. I contrast the various classical limits which emerge from the different ways of assessing teleportation. An obvious omission from the list of continuous variable quantum information manipulations is any proposal for direct analogues of 2 photon interference effects, especially those that lead to Bell inequality type tests of local realism. Bell-type correlations are the defining feature of discrete variable entanglement experimentally. I discuss new work that shows how entanglement of the Bell-type can be observed in continuous variable, homodyne measurement schemes.
Quantum teleportation is one of the most fundamental subjects in quantum information technology. This is because quantum teleportation can be used as not only a communication network but also a building block for universal quantum information processing. It is well known that there are two approaches (i. e. discrete and continuous variable approaches) in quantum information processing. In particular, continuous variable one has some advantages, that is, capability for deterministic and efficient quantum operations. In the case of continuous variable quantum teleportation, however, we cannot teleport quantum states perfectly due to finite level of quadrature squeezed states. Hence it is important to improve the fidelity of teleportation to realize more advanced quantum network and circuits. Thanks to the recent improvement of squeezing level, fidelity up to F=0.83 has been achieved. In this article, we review the experiment of high fidelity quantum teleportation for continuous variables, and its applications.
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).
Abstract Quantum network scales the advantages of quantum communication protocols to more than two detached users, which offers great potential to realize the quantum internet. Here, a fully connected continuous‐variable (CV) quantum teleportation network architecture is presented, in which a squeezed state of light distributes each pair of entangled sideband modes to each communication link that bridges any pair of users. The quantum teleportation scheme is similar to standard two‐party ones for each communication link, without sacrificing communication capability and reliability. The demonstration based on CV‐entangled sideband modes opens an innovative possibility to implement many tasks of deterministic quantum information processing.