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The Quantum Internet, by enabling quantum communications among remote quantum nodes, is a network capable of supporting functionalities with no direct counterpart in the classical world. Indeed, with the network and communications functionalities provided by the Quantum Internet, remote quantum devices can communicate and cooperate for solving challenging computational tasks by adopting a distributed computing approach. The aim of this study is to provide the reader with an overview about the main challenges and open problems arising in the design of a distributed quantum computing ecosystem. For this, the authors provide a survey, following a bottom-up approach, from a communications engineering perspective. They start by introducing the Quantum Internet as the fundamental underlying infrastructure of the distributed quantum computing ecosystem. Then they go further, by elaborating on a high-level system abstraction of the distributed quantum computing ecosystem. They describe such an abstraction through a set of logical layers. Thereby, they clarify dependencies among the aforementioned layers and, at the same time, a road-map emerges.

In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound, and Caratheodory's treatment of the second law of thermodynamics. All mathematical derivations are based on clear physical pictures which make even the most involved results — such as the Holevo bound — look comprehensible and transparent. Quantum information is a fascinating topic precisely because it shows that the laws of information processing are actually dependent on the laws of physics. However, it is also very interesting to see that information theory has something to teach us about physics. Both of these directions are discussed throughout the book. Other topics covered in the book are quantum mechanics, measures of quantum entanglement, general conditions of quantum error correction, pure state entanglement and Pauli matrices, pure states and Bell's inequalities, and computational complexity of quantum algorithms.

A quantum channel is a physical media able to carry quantum signals. Quantum key distribution (QKD) requires direct quantum channels between every pair of prepare-and-measure modules. This requirement heavily compromises the scalability of networks of directly connected QKD modules. A way to avoid this problem is to introduce switches that can dynamically reconfigure the set of connections. The reconfiguration of a quantum channel implies that the modules using it can adapt to the new channel and peer.The maturity and flexibility of continuous-variable QKD (CV-QKD) qualifies it as a strong contender for integration into optical communication networks. Here we present the implementation of a switched CV-QKD network embedded in the Madrid quantum testbed. The optical switching of the quantum paths significantly reduces the amount of required QKD modules and facilitates the scalability of the network. This demonstration highlights the flexibility and ease of integration of this emerging technology.

Modern optical communication technology can realize a large-scale multilevel (or M-ary) optical signal. Investigating the quantum mechanical nature of such a large-scale M-ary optical signal is essential for a unified understanding of quantum information science and optical communication technology. This article focuses on the quantum-mechanical non-orthogonality for a collection of pure quantum states and proposes a non-orthogonality index based on the least squares error criterion in quantum detection theory. First, we define the index for linearly independent signals, and the proposed index is analyzed through numerical simulations. Next, the index is applied to a highly large-scale M-ary phase-shift keying (PSK) coherent state signal. Furthermore, the index is compared with the capacity of the pure state channel with the PSK signal. As a result, it is shown that a highly large-scale M-ary PSK coherent state signal exhibits a quantum nature even when the signal transmission power is very high. Thus, the theoretical characterization of a highly large-scale M-ary coherent state signal based on the proposed index will be the first step toward a better understanding of cutting-edge optical communication technologies such as the quantum stream cipher Y00.

We present and analyze an architecture for a European-scale quantum network using satellite links to connect Quantum Cities, which are metropolitan quantum networks with minimal hardware requirements for the end users. Using NetSquid, a quantum network simulation tool based on discrete events, we assess and benchmark the performance of such a network linking distant locations in Europe in terms of quantum key distribution rates, considering realistic parameters for currently available or near-term technology. Our results highlight the key parameters and the limits of current satellite quantum communication links and can be used to assist the design of future missions. We also discuss the possibility of using high-altitude balloons as an alternative to satellites.

An arbitrary amount of entanglement shared among nodes of a quantum network might be nondistillable if the nodes lack the information on the entangled Bell pairs they share. Making such a system distillable, which is called the superactivation of bound entanglement (BE), was shown to be possible through systematic quantum teleportation between the nodes, requiring the implementation of controlled-gates scaling with the number of nodes. In this work, we show in two scenarios that the superactivation of BE is possible if nodes implement the proposed local quantum Zeno strategies based on only single qubit rotations and simple threshold measurements. In the first scenario we consider, we obtain a two-qubit distillable entanglement system as in the original superactivation proposal. In the second scenario, we show that superactivation can be achieved among the entire network of eight qubits in five nodes. In addition to obtaining all-particle distillable entanglement, the overall entanglement of the system in terms of the sum of bipartite cuts is increased. We also design a general algorithm with variable greediness for optimizing the QZD evolution tasks. Implementing our algorithm for the second scenario, we show that a significant improvement can be obtained by driving the initial BE system into a maximally entangled state. We believe our work contributes to quantum technologies from both practical and fundamental perspectives bridging nonlocality, bound entanglement and the quantum Zeno dynamics among a quantum network.

We discuss principles of measuring a topological charge or representation that travels in a set of anyons. We describe the procedure and analyze how it works for different values of theory parameters. We also show how it can be modified to be more efficient.

As a novel paradigm in quantum communication, quantum secure direct communication (QSDC) enables secure, reliable, and deterministic information transmission, leveraging the principles of quantum mechanics. One-photon-interference QSDC is particularly attractive because it mitigates the vulnerabilities in measurement devices while extending transmission distances. In this paper, we propose a high-dimensional one-photon-interference QSDC protocol that exploits the advantages of high-dimensional encoding in the phase of weak coherent pluses to further enhance transmission distances and improve secrecy channel capacity. The security of this protocol is analyzed using quantum wiretap channel theory, and its resistance to common quantum threats is discussed. Numerical simulations demonstrate that our protocol outperforms its predecessor in terms of its secrecy capacity and extends the maximum communication distance achievable up to 494 km, which is over 13% longer than the two-dimensional case, effectively doubling the transmission length of traditional protocols. These improvements highlight the protocol’s potential for use in quantum communication applications in this era of frequent data breaches and information leaks.

Quantum secure direct communication (QSDC) transmits information directly over a quantum channel. In addition to security in transmission, it avoids loopholes of key loss and prevents the eavesdropper from getting ciphertext. In this article, we propose a QSDC protocol using entangled photon pairs. This protocol differs from existing entanglement-based QSDC protocols because it does not perform Bell-state measurement, and one photon of the entangled pair is measured after the entanglement distribution. It has the advantage of high signal-to-noise ratio due to the heralding function of entanglement pairs, and it also has the relative ease in performing single-photon measurement. The protocol can use a practical entanglement source from spontaneous parametric down-conversion (SPDC); Gottesman-Lo-Lütkenhaus-Preskill theory and the decoy state method give a better estimate of the error rate. Security analysis is completed with Wyner’s wiretap channel theory, and the lower bound of the secrecy capacity is estimated. Numerical simulations were carried out to study the performance of the protocol. These simulations demonstrated that the protocol with a practical SPDC entanglement source performed well and was close to the case with an ideal entanglement source.