Quantum key distribution is widely thought to offer unconditional security in communication between two users. Unfortunately, a widely accepted proof of its security in the presence of source, device and channel noises has been missing. This long-standing problem is solved here by showing that, given fault-tolerant quantum computers, quantum key distribution over an arbitrarily long distance of a realistic noisy channel can be made unconditionally secure. The proof is reduced from a noisy quantum scheme to a noiseless quantum scheme and then from a noiseless quantum scheme to a noiseless classical scheme, which can then be tackled by classical probability theory. * This reprint version contains the same material as the one published in Science , 2050-2056 (1999). 283We also include the refereed supplementary notes (as in http://www.sciencemag.org/feature/data/984035.shl) explicitly in the appendix for easy reference. †

We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the source and detector are under the limited control of an adversary. Our proof applies when both the source and the detector have small basis-dependent flaws, as is typical in practical implementations of the protocol. We derive a general lower bound on the asymptotic key generation rate for weakly basis-dependent eavesdropping attacks, and also estimate the rate in some special cases: sources that emit weak coherent states with random phases, detectors with basis-dependent efficiency, and misaligned sources and detectors.

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.

Quantum key distribution (QKD) promises unconditional security in data communication and is currently being deployed in commercial applications. Nonetheless, before QKD can be widely adopted, it faces a number of important challenges such as secret key rate, distance, size, cost and practical security. Here, we survey those key challenges and the approaches that are currently being taken to address them. For thousands of years, human beings have been using codes to keep secrets. With the rise of the Internet and recent trends to the Internet of Things, our sensitive personal financial and health data as well as commercial and national secrets are routinely being transmitted through the Internet. In this context, communication security is of utmost importance. In conventional symmetric cryptographic algorithms, communication security relies solely on the secrecy of an encryption key. If two users, Alice and Bob, share a long random string of secret bits-the key-then they can achieve unconditional security by encrypting their message using the standard one-time-pad encryption scheme. The central question then is: how do Alice and Bob share a secure key in the first place? This is called the key distribution problem. Unfortunately, all classical methods to distribute a secure key are fundamentally insecure because in classical physics there is nothing preventing an eavesdropper, Eve, from copying the key during its transit from Alice to Bob. On the other hand, standard asymmetric or public-key cryptography solves the key distribution problem by relying on computational assumptions such as the hardness of factoring. Therefore, such schemes do not provide information-theoretic security because they are vulnerable to future advances in hardware and algorithms, including the construction of a large-scale quantum computer.

To increase dramatically the distance and the secure key generation rate of quantum key distribution (QKD), the idea of quantum decoys-signals of different intensities -has recently been proposed. Here, we present the first experimental implementation of decoy state QKD. By making simple modifications to a commercial quantum key distribution system, we show that a secure key generation rate of 165 bit=s, which is 1=4 of the theoretical limit, can be obtained over 15 km of a telecommunication fiber. We also show that with the same experimental parameters, not even a single bit of secure key can be extracted with a non-decoy-state protocol. Compared to building single photon sources, decoy state QKD is a much simpler method for increasing the distance and key generation rate of unconditionally secure QKD. DOI: 10.1103/PhysRevLett.96.070502 PACS numbers: 03.67.Dd, 42.50.Dv Quantum key distribution (QKD) [1,2] was proposed as a method of achieving perfectly secure communications. Any eavesdropping attempt by a third party will necessarily introduce an abnormally high quantum bit error rate in a quantum transmission and thus be caught by the users. With a perfect single photon source, QKD provides proven unconditional security guaranteed by the fundamental laws of quantum physics [3,4].Most current experimental QKD setups are based on attenuated laser pulses which occasionally give out multiphotons. Therefore, any security proofs must take into account the possibility of subtle eavesdropping attacks, including the photon-number splitting attack [5]. A hallmark of those subtle attacks is that they introduce a photonnumber dependent attenuation to the signal. Fortunately, it is still possible to obtain unconditionally secure QKD, even with (phase randomized) attenuated laser pulses, as theoretically demonstrated in [6] and by Gottesman-Lo-Lütkenhaus-Preskill (GLLP) [7]. However, one must pay a steep price by placing severe limits on the distance and the key generation rate. See also [8].A key question is this: How can one extend the distance and key generation rate of secure QKD? A brute force solution to this problem would be to use a (nearly) perfect single photon source. Despite much experimental effort [9], reliable perfect single photon sources are far from practical.Another solution to increase the transmission distance and key generation rate is to employ decoy states, using extra states of different average photon number to detect photon-number dependent attenuation. It has attracted great recent interest. The decoy method was first discovered by Hwang [10]. In [11], we presented the first rigorous security proof of decoy state QKD. We showed that the decoy state method can be combined with the standard GLLP result to achieve dramatically higher key generation rates and distances. Moreover, we proposed practical protocols with vacua or weak coherent states as decoys. Subsequently, the security of practical protocols have been analyzed by Wang [12] and us [13]. See also [14]. In particular, we [13] demonstr...

We study the amount of classical communication needed for distributed quantum information processing. In particular, we introduce the concept of "remote preparation" of a quantum state. Given an ensemble of states, Alice's task is to help Bob in a distant laboratory to prepare a state of her choice. We find several examples of an ensemble with an entropy S where the remote preparation can be done with a communication cost lower than the amount (2S) required by standard teleportation. We conjecture that, for an arbitrary N -dimensional pure state, its remote preparation requires 2log 2 N bits of classical communication, as in standard teleportation.

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.

We study the existence of absolutely maximally entangled (AME) states in quantum mechanics and its applications to quantum information. AME states are characterized by being maximally entangled for all bipartitions of the system and exhibit genuine multipartite entanglement. With such states, we present a novel parallel teleportation protocol which teleports multiple quantum states between groups of senders and receivers. The notable features of this protocol are that (i) the partition into senders and receivers can be chosen after the state has been distributed, and (ii) one group has to perform joint quantum operations while the parties of the other group only have to act locally on their system. We also prove the equivalence between pure state quantum secret sharing schemes and AME states with an even number of parties. This equivalence implies the existence of AME states for an arbitrary number of parties based on known results about the existence of quantum secret sharing schemes. PACS numbers:Introduction. Entanglement is at the core of the power of quantum information processing and has been extensively studied for few qubits. The classification of entanglement classes for three and four qubits is well understood [1][2][3][4][5][6][7] and canonical forms of pure states under local unitary transformations of each local Hilbert space have also been analyzed [6,8,9]. As the number of local quantum degrees of freedom increases, our understanding of entanglement gets poorer. The number of independent invariants that classify entanglement grows exponentially and it is unclear which purpose each category of entanglement serves [10,11]. In recent years, there has been an important progress in the classification of the maximally multipartite entangled states composed of qubits [7,[12][13][14][15]. Nevertheless, a complete understanding of the structure, classification and usefulness of quantum states with the largest possible entanglement for arbitrary dimension is still missing. Another motivation for studying multipartite entanglement is its connection to other apparently unrelated areas of physics, like string theory and black-holes [16,17].Quantum teleportation is one of the most intriguing utilizations of entanglement. It allows distant parties, who share a resource of entanglement, to transport a quantum state from one party to the other by only exchanging classical information and using up said entanglement. The first proposal of such a protocol used the resource of bipartite entanglement between two parties [18]. Later teleportation protocols using genuine multipartite entanglement between more than two parties were proposed theoretically for four qubit entanglement [19], and experimentally in the form of open-destination teleportation for five qubits [20].This manuscript is devoted to initiate the study of a class of states with genuine multipartite entanglement. These states, which we call absolutely maximally entangled (AME) states, are defined as having the strict maximal entanglement in all