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)  allows two distant parties, Alice and Bob, to distribute a secret key, which is essential to achieve provable secure communications . 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 . Importantly, Gottesman, Lo, Lütkenhaus and Preskill  (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 . 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
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 . So far, the main interest in the quantum internet has been its realization . 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  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  that existing intercity quantum key distribution (QKD) protocols  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  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...
In theory, quantum key distribution (QKD) offers information-theoretic security. In practice, however, it does not due to the discrepancies between the assumptions used in the security proofs and the behavior of the real apparatuses. Recent years have witnessed a tremendous effort to fill the gap, but the treatment of correlations among pulses has remained a major elusive problem. Here, we close this gap by introducing a simple yet general method to prove the security of QKD with arbitrarily long-range pulse correlations. Our method is compatible with those security proofs that accommodate all the other typical device imperfections, thus paving the way toward achieving implementation security in QKD with arbitrary flawed devices. Moreover, we introduce a new framework for security proofs, which we call the reference technique. This framework includes existing security proofs as special cases, and it can be widely applied to a number of QKD protocols.
We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not restricted. Although our result follows the idea of Azuma et al (2016 Nat. Commun. 7 13523) of splitting the network into two parts, our approach relaxes their strong restriction, consisting of the use of a single entanglement measure in the quantification of the maximum amount of entanglement generated by the channels. In particular, in our bound the measure can be chosen on a channel-by-channel basis, in order to make it as tight as possible. This enables us to apply the relative entropy of entanglement, which often gives a state-of-the-art upper bound, on every Choi-simulable channel in the network, even when the other channels do not satisfy this property. We also develop tools to compute, or bound, the max-relative entropy of entanglement for channels that are invariant under phase rotations. In particular, we present an analytical formula for the max-relative entropy of entanglement of the qubit amplitude damping channel. IntroductionWhenever two parties, say Alice and Bob, want to communicate by using a quantum channel, its noise unavoidably limits their communication efficiency . In the limit of many channel uses, their asymptotic optimal performance can be quantified by the channel capacity, which represents the supremum of the number of qubits/bits that can be faithfully transmitted per channel use. Obtaining an exact expression for this quantity is typically far from trivial. Indeed, in addition to the difficulty of studying the asymptotic behaviour of the channel, the value of the capacity also depends on the task Alice and Bob want to perform, as well as on the free resources available to them . Two representative tasks, which will be considered in our paper, involve the generation and distribution of a string of shared private bits (pbits) [2,3] or of maximally entangled states (ebits) . These are known to be fundamental resources for more complex protocols, such as secure classsical communication [5,6], quantum teleportation , and quantum state merging . An example of free resource involves the possibility of exchanging classical information over a public classical channel, such as a telephone line or over the internet. Depending on the restrictions on this, the capacity is said to be assisted by zero, forward, backward, or two-way classical communication . In this paper we will focus on the last option, that is, no restriction will be imposed on the use of classical communication.Although the capacity of a quantum channel is by definition an abstract and theoretical quantity, it is also practically useful in that it can be compared with the performance of known transmission schemes. This comparison could then give an indication on the extent of improvements that could be expected in the future. From this perspective, similar conclusions could be obt...
Despite the enormous theoretical and experimental progress made so far in quantum key distribution (QKD), the security of most existing QKD implementations is not rigorously established yet. A critical obstacle is that almost all existing security proofs make ideal assumptions on the QKD devices. Problematically, such assumptions are hard to satisfy in the experiments, and therefore it is not obvious how to apply such security proofs to practical QKD systems. Fortunately, any imperfections and security-loopholes in the measurement devices can be perfectly closed by measurement-device-independent QKD (MDI-QKD), and thus we only need to consider how to secure the source devices. Among imperfections in the source devices, correlations between the sending pulses are one of the principal problems. In this paper, we consider a setting-choice-independent correlation (SCIC) framework in which the sending pulses can present arbitrary correlations but they are independent of the previous setting choices such as the bit, the basis and the intensity settings. Within the framework of SCIC, we consider the dominant fluctuations of the sending states, such as the relative phases and the intensities, and provide a self-contained information theoretic security proof for the loss-tolerant QKD protocol in the finite-key regime. We demonstrate the feasibility of secure quantum communication within a reasonable number of pulses sent, and thus we are convinced that our work constitutes a crucial step toward guaranteeing implementation security of QKD.
The correlation functions of the spin-1/2 XXZ chain in the ground state were expressed in the form of multiple integrals for −1 < ∆ ≤ 1 and 1 < ∆. In particular, adjacent four-point correlation functions were given as certain four-dimensional integrals. We show that these integrals can be reduced to polynomials with respect to specific one-dimensional integrals. The results give the polynomial representation of the third-neighbor correlation functions.
Quantum networks will allow to implement communication tasks beyond the reach of their classical counterparts. A pressing and necessary issue for the design of quantum network protocols is the quantification of the rates at which these tasks can be performed. Here, we propose a simple recipe that yields efficiently computable lower and upper bounds for network capacities. For this we make use of the max-flow min-cut theorem and its generalization to multi-commodity flows to obtain linear programs (LPs). We exemplify our recipe deriving the LPs for bipartite settings, settings where multi-pairs of users obtain entanglement in parallel as well as multipartite settings, covering almost all known situations. We also make use of a generalization of the concept of paths between user pairs in a network to Steiner trees spanning the group of users wishing to establish GHZ states. Contents 26A. Proof of Lemma 2 26 B. Proof of Lemma 3 27 C. Proof of Lemma 4 28 arXiv:1809.03120v2 [quant-ph] 4 Jan 2019 total/worst case network and P total/worst case networkas the maximum rate achievable by means of an adaptive protocol, as well as (3) the maximization over a weighted sum of rates over all user pairs. From [13,14], we can obtain upper bounds on the private capacities that involve (1) a minimization over multicuts, i.e. sets of edges the removal of which connects all pairs, or (2) the so-called minimum cut ratio . Using the respective results of [17,19], we can, up to a factor of order O(log r), upper bound the capacities for both cases (1) and (2) by a maximization over concurrent multi-commodity flows, i.e. flows between several user pairs that can be achieved in parallel. In the first case we maximize the sum of flows for all user pairs, whereas in the second case we maximize the worst case flow that is guaranteed for every pair. Both multi-commodity flow maximizations can be cast into LPs. Applying the aggregated repeater protocol  to multiple user pairs we also obtain lower bounds in terms of the maximum concurrent multi-commodity flows, providing us with the following efficiently computable bounds: f total/worst case Q ↔ ≤ Q total/worst case network ≤ P total/worst case network ≤ O(log r)f total/worst case Esq/E
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