Quantum communication holds promise for unconditionally secure transmission of secret messages and faithful transfer of unknown quantum states. Photons appear to be the medium of choice for quantum communication. Owing to photon losses, robust quantum communication over long lossy channels requires quantum repeaters. It is widely believed that a necessary and highly demanding requirement for quantum repeaters is the existence of matter quantum memories. Here we show that such a requirement is, in fact, unnecessary by introducing the concept of all-photonic quantum repeaters based on flying qubits. In particular, we present a protocol based on photonic cluster-state machine guns and a loss-tolerant measurement equipped with local high-speed active feedforwards. We show that, with such all-photonic quantum repeaters, the communication efficiency scales polynomially with the channel distance. Our result paves a new route towards quantum repeaters with efficient single-photon sources rather than matter quantum memories.

In principle, quantum key distribution (QKD) offers unconditional security based on the laws of physics. In practice, flaws in the state preparation undermine the security of QKD systems, as standard theoretical approaches to deal with state preparation flaws are not loss-tolerant. An eavesdropper can enhance and exploit such imperfections through quantum channel loss, thus dramatically lowering the key generation rate. Crucially, the security analyses of most existing QKD experiments are rather unrealistic as they typically neglect this effect. Here, we propose a novel and general approach that makes QKD loss-tolerant to state preparation flaws. Importantly, it suggests that the state preparation process in QKD can be significantly less precise than initially thought. Our method can widely apply to other quantum cryptographic protocols.PACS numbers: 03.67.Dd, 03.67.-a Introduction.-Quantum key distribution (QKD) [1] allows two distant parties, Alice and Bob, to distribute a secret key, which is essential to achieve provable secure communications [2]. The field of QKD has progressed very rapidly over the last years, and it now offers practical systems that can operate in realistic environments [3,4].Crucially, QKD provides unconditional security based on the laws of physics, i.e., despite the computational power of the eavesdropper, Eve. Indeed, the security of QKD has been promptly demonstrated for different scenarios [5][6][7][8][9][10][11][12]. Importantly, Gottesman, Lo, Lütkenhaus and Preskill [13] (henceforth referred to as GLLP) proved the security of QKD when Alice's and Bob's devices are flawed, as is the case in practical implementations. Unfortunately, however, GLLP has a severe limitation, namely, it is not loss-tolerant; it assumes the worst case scenario where Eve can enhance flaws in the state preparation by exploiting channel loss. As a result, the key generation rate and achievable distance of QKD are dramatically reduced [14]. Notice that most existing QKD experiments simply ignore state preparation imperfections in their key rate formula, which renders their results unrealistic and not really secure.In this Letter, we show that GLLP's worst case assumption is far too conservative, i.e., in sharp contrast to GLLP, we present a security proof for QKD that is loss-tolerant. Indeed, for the case of modulation errors, an important flaw in real-life QKD systems, we show that Eve cannot exploit channel loss to enhance such imperfections. The intuition here is rather simple: in this type of state preparation flaws the signals sent out by Alice are still qubits, i.e., there is no side-channel for Eve to exploit

Most quantum communication tasks need to rely on the transmission of quantum signals over long distances. Unfortunately, transmission of such signals is most often limited by losses in the channel, the same issue that affects classical communication. Simple signal amplification provides an elegant solution for the classical world, but this is not possible in the quantum world, as the no-cloning theorem forbids such an operation and, thus, an alternative approach, a quantum repeater, is needed. Quantum repeaters enable one to create a known maximally entangled state between the end points of the network by first segmenting the network into pieces, creating entanglement between the segments, and then, connecting those entanglement to create the required long range entanglement. Quantum teleportation then allows an unknown quantum message to be transmitted between them using the long-range entangled state. This form of quantum communication will be at the heart of the future quantum Internet. In this review, we will detail various approaches to quantum repeaters, and discuss their expected performance and limitations.

Twin-field (TF) quantum key distribution (QKD) was conjectured to beat the private capacity of a point-to-point QKD link by using single-photon interference in a central measuring station. This remarkable conjecture has recently triggered an intense research activity to prove its security. Here, we introduce a TF-type QKD protocol which is conceptually simpler than the original proposal. It relies on the pre-selection of a global phase, instead of the post-selection of a global phase, which significantly simplifies its security analysis and is arguably less demanding experimentally. We demonstrate that the secure key rate of our protocol has a square-root improvement over the point-to-point private capacity, as conjectured by the original TF QKD.

The quantum internet holds promise for achieving quantum communication—such as quantum teleportation and quantum key distribution (QKD)—freely between any clients all over the globe, as well as for the simulation of the evolution of quantum many-body systems. The most primitive function of the quantum internet is to provide quantum entanglement or a secret key to two points efficiently, by using intermediate nodes connected by optical channels with each other. Here we derive a fundamental rate-loss trade-off for a quantum internet protocol, by generalizing the Takeoka–Guha–Wilde bound to be applicable to any network topology. This trade-off has essentially no scaling gap with the quantum communication efficiencies of protocols known to be indispensable to long-distance quantum communication, such as intercity QKD and quantum repeaters. Our result—putting a practical but general limitation on the quantum internet—enables us to grasp the potential of the future quantum internet.

Recent field demonstrations of quantum key distribution (QKD) networks hold promise for unconditionally secure communication. However, owing to loss in optical fibres, the length of point-to-point links is limited to a hundred kilometers, restricting the QKD networks to intracity. A natural way to expand the QKD network in a secure manner is to connect it to another one in a different city with quantum repeaters. But, this solution is overengineered unless such a backbone connection is intercontinental. Here we present a QKD protocol that could supersede even quantum repeaters for connecting QKD networks in different cities below 800 km distant. Nonetheless, in contrast to quantum repeaters, this protocol uses only a single intermediate node with optical devices, requiring neither quantum memories nor quantum error correction. Our all-photonic ‘intercity' QKD protocol bridges large gaps between the conventional intracity QKD networks and the future intercontinental quantum repeaters, conceptually and technologically.

Twin-field (TF) quantum key distribution (QKD) was conjectured to beat the private capacity of a point-to-point QKD link by using single-photon interference in a central measuring station. This remarkable conjecture has recently triggered an intense research activity to prove its security. Here, we introduce a TF-type QKD protocol which is conceptually simpler than the original proposal. It relies on local phase randomization, instead of global phase randomization, which significantly simplifies its security analysis and is arguably less demanding experimentally. We demonstrate that the secure key rate of our protocol has a square-root improvement over the point-to-point private capacity, as conjectured by the original TF-QKD scheme.

The quantum internet holds promise for performing quantum communication, such as quantum teleportation and quantum key distribution, freely between any parties all over the globe. For such a quantum internet protocol, a general fundamental upper bound on the performance has been derived [K. Azuma, A. Mizutani, and H.-K. Lo, arXiv:1601.02933]. Here we consider its converse problem. In particular, we present a protocol constructible from any given quantum network, which is based on running quantum repeater schemes in parallel over the network. The performance of this protocol and the upper bound restrict the quantum capacity and the private capacity over the network from both sides. The optimality of the protocol is related to fundamental problems such as additivity questions for quantum channels and questions on the existence of a gap between quantum and private capacities.PACS numbers: 03.67. Hk, 03.67.Dd, 03.65.Ud, In the Internet, if a client communicates with a far distant client, the data travel across multiple networks. At present, the nodes and the communication channels in the networks are composed of physical devices governed by the laws of classical information theory, and the data flow obeys the celebrated max-flow min-cut theorem in graph theory. However, in the future, such classical nodes and channels should be replaced with quantum ones, whose network follows the rules of quantum information theory, rather than classical one. This network, called quantum internet, could accomplish tasks that are intractable in the realm of classical information processing, and it serves opportunities and challenges across a range of intellectual and technical frontiers, including quantum communication, computation, metrology, and simulation [1]. So far, the main interest in the quantum internet has been its realization [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. But, it must be one of the most fundamental trials from a theoretical perspective to grasp the full potential of the quantum internet. Along this line, recently, a general fundamental upper bound on the performance was derived [17] for its use for supplying two clients with entanglement or a secret key. Interestingly, this upper bound is estimable and applied to any private-key or entanglement distillation scheme that works over any network topology composed of arbitrary quantum channels by using arbitrary local operations and unlimited classical communication (LOCC). With this, for the case of linear lossy optical channel networks, it has been shown [17] that existing intercity quantum key distribution (QKD) protocols [18][19][20] and quantum repeater schemes [7,8,12,14,15] have no scaling gap with the fundamental upper bound. Moreover, in the case of a multipath network composed of a wide range of stretchable quantum channels (including lossy optical channels), it has been proven [21] to be optimal to choose a single path between two clients for running quantum repeater scheme, in order to minimize the number of times paths between them are used...