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We investigate quantum key distribution (QKD) in optical multiple-input-multiple-output (MIMO) settings. Such settings can prove useful in dealing with harsh channel conditions as in, e.g., satellite-based QKD. We study a $2\times2$ setting for continuous variable (CV) QKD with Gaussian encoding and heterodyne detection and reverse reconciliation. We present our key rate analysis for this system and compare it with single-mode and multiplexed CV QKD scenarios. We show that we can achieve multiplexing gain using multiple transmitters and receivers even if there is some crosstalk between the two channels. In certain cases, when there is nonzero correlated excess noise in the two received signals, we can even surpass the multiplexing gain.

The security of prepare-and-measure satellite-based quantum key distribution (QKD), under restricted eavesdropping scenarios, is addressed. We particularly consider cases where the eavesdropper, Eve, has limited access to the transmitted signal by Alice, and/or Bob's receiver station. This restriction is modeled by lossy channels between Alice/Bob and Eve, where the transmissivity of such channels can, in principle, be bounded by monitoring techniques. An artefact of such lossy channels is the possibility of having {\it bypass} channels, those which are not accessible to Eve, but may not necessarily be characterized by the users either. This creates interesting, unexplored, scenarios for analyzing QKD security. In this paper, we obtain generic bounds on the key rate in the presence of bypass channels and apply them to continuous-variable QKD protocols with Gaussian encoding with direct and reverse reconciliation. We find regimes of operation in which the above restrictions on Eve can considerably improve system performance. We also develop customised bounds for several protocols in the BB84 family and show that, in certain regimes, even the simple protocol of BB84 with weak coherent pulses is able to offer positive key rates at high channel losses, which would otherwise be impossible under an unrestricted Eve. In this case the limitation on Eve would allow Alice to send signals with larger intensities than the optimal value under an ideal Eve, which effectively reduces the effective channel loss. In all these cases, the part of the transmitted signal that does not reach Eve can play a non-trivial role in specifying the achievable key rate. Our work opens up new security frameworks for spaceborne quantum communications systems., Comment: 26 pages, 17 figures

Quantum technologies are increasingly recognized as groundbreaking advancements set to redefine the landscape of computing, communications, and sensing by leveraging quantum phenomena, like entanglement and teleportation. Quantum technologies offer an interesting set of advantages such as unconditional security, large communications capacity, unparalleled computational speed, and ultra-precise sensing capabilities. However, their global deployment faces challenges related to communication ranges and geographical boundaries. Non-terrestrial networks (NTNs) have emerged as a potential remedy for these challenges through providing free-space quantum links to circumvent the exponential losses inherent in fiber optics. This paper delves into the dynamic interplay between quantum technologies and NTNs to unveil their synergistic potential. Specifically, we investigate their integration challenges and the potential solutions to foster a symbiotic convergence of quantum and NTN functionalities while identifying avenues for enhanced interoperability. This paper not only offers useful insights into the mutual advantages but also presents future research directions, aiming to inspire additional studies and advance this interdisciplinary collaboration.

We investigate the use of high-dimensional quantum key distribution (HD-QKD) in wireless access to hybrid quantum classical networks. We study the distribution of d-dimensional time-phase encoded states between an indoor wireless user and the central office on the other end of the access network. We evaluate the performance in the case of transmitting quantum and classical signals over the same channel by accounting for the impact of background noise induced by the Raman-scattered light on the QKD receiver. We also take into account the loss and background noise that occur in indoor environments as well as finite key effects in our analysis. We show that an HD-QKD system with d = 4 can outperform its qubit-based counterpart., Comment: 7 pages, 6 figures

We investigate quantum repeater protocols that rely on three-qubit repetition codes using nitrogen-vacancy (NV) centers in diamond as quantum memories. NV centers offer a two-qubit register, corresponding to their electron and nuclear spins, which makes it possible to perform deterministic two-qubit operations within one NV center. For quantum repeater applications, we, however, need to do joint operations on two separate NV centers. Here, we study two NV-center based repeater structures that enable such deterministic joint operations. One structure offers less consumption of classical communication, at the cost of more computation overhead, whereas the other one relies on a fewer number of physical resources and operations. We assess and compare their performance for the task of secret key generation under the influence of noise and decoherence with current and near-term experimental parameters. We quantify the regimes of operation, where one structure outperforms the other, and find the regions where encoded quantum repeaters offer practical advantages over their non-encoded counterparts., Comment: 14 pages, 6 figures

We study the implementation of quantum key distribution (QKD) systems over quantum repeater infrastructures. We particularly consider quantum repeaters with encoding and compare them with probabilistic quantum repeaters. To that end, we propose two decoder structures for encoded repeaters that not only improve system performance but also make the implementation aspects easier by removing two-qubit gates from the QKD decoder. By developing several scalable numerical and analytical techniques, we then identify the resilience of the setup to various sources of error in gates, measurement modules, and initialization of the setup. We apply our techniques to three- and five-qubit repetition codes and obtain the normalized secret key generation rate per memory per second for encoded and probabilistic quantum repeaters. We quantify the regimes of operation, where one class of repeater outperforms the other, and find that there are feasible regimes of operation where encoded repeaters -- based on simple three-qubit repetition codes -- could offer practical advantages., Comment: 15 pages, 10 figures

Twin-field (TF) quantum key distribution (QKD) can overcome fundamental secret-key-rate bounds on point-to-point QKD links, allowing us to reach longer distances than ever before. Since its introduction, several TF-QKD variants have been proposed, and some of them have already been implemented experimentally. Most of them assume that the users can emit weak coherent pulses with a continuous random phase. In practice, this assumption is often not satisfied, which could open up security loopholes in their implementations. To close this loophole, we propose and prove the security of a TF-QKD variant that relies exclusively on discrete phase randomisation. Remarkably, our results show that it can also provide higher secret-key rates than counterpart protocols that rely on continuous phase randomisation.

We propose a post-selection technique, based on quantum error detection, for quantum key distribution (QKD) systems that run over quantum repeaters with encoding. In such repeaters, quantum error correction techniques are used for entanglement distillation. By developing an analytical approach to study such quantum repeaters, we show that, in the context of QKD, it is often more efficient to use the error detection, rather than the error correction, capability of the underlying code to sift out cases where an error has been detected. We implement our technique for three-qubit repetition codes by modelling different sources of error in crucial components of the system. We then investigate in detail the impact of such imperfections on the secret key generation rate of the QKD system, and how one can use the information obtained during entanglement swapping and decoding stages to maximize the rate. For benchmarking purposes, we specify the maximum allowed error rates in different components of the setup below which positive key rates can be obtained., Comment: 14 pages, 7 figures

Memory-assisted quantum key distribution (MA-QKD) systems are among novel promising solutions that can improve the key-rate scaling with channel loss. By using a middle node with quantum storage and measurement functionalities, they offer the same key-rate scaling with distance as a single-node quantum repeater. However, the distance at which they can surpass the nominal key rate of repeaterless systems, in terms of bits per second, is typically long, owing to the efficiency and/or interaction time issues when one deals with quantum memories. This crossover distance can be a few hundred kilometres, for instance, when one relies on the exchange of infinitely many key bits for the key-rate analysis. In a realistic setup, however, we should account for the finite-key effects in our analysis. Here, we show that accounting for such effects would actually favour MA-QKD setups, by reducing the crossover distance to the regime where realistic implementations can take place. We demonstrate this by rigorously analysing a decoy-state version of MA-QKD, in the finite-key regime, using memory parameters already achievable experimentally. This provides us with a better understanding of the advantages and challenges of working with memory-based systems., Comment: 23 pages, 4 figures. v2: Updated to accepted version

Quantum key distribution (QKD) offers a reliable solution to communication problems that require long-term data security. For its widespread use, however, the rate and reach of QKD systems must be improved. Twin-field (TF) QKD is a step forward toward this direction, with early demonstrations suggesting it can beat the current rate-versus-distance records. A recently introduced variant of TF-QKD is particularly suited for experimental implementation, and has been shown to offer a higher key rate than other variants in the asymptotic regime where users exchange an infinite number of signals. Here, we extend the security of this protocol to the finite-key regime, showing that it can overcome the fundamental bounds on point-to-point QKD with around $10^{10}$ transmitted signals. Within distance regimes of interest, our analysis offers higher key rates than those of alternative variants. Moreover, some of the techniques we develop are applicable to the finite-key analysis of other QKD protocols., Comment: 26 pages, 5 figures. v2: major changes on subsection "Concentration inequality for sums of dependent random variables", minor changes elsewhere. v3: Changes on subsection "Concentration inequality for sums of dependent random variables", to use the newest version of the inequality in Ref. [38]. Minor changes in citations elsewhere. v4: Fixed wrong citation numbers in graph legends

Recently, a quantum multi-party summation protocol based on the quantum Fourier transform has been proposed [Quantum Inf Process 17: 129, 2018]. The protocol claims to be secure against both outside and participant attacks. However, a closer look reveals that the player in charge of generating the required multi-partite entangled states can launch two kinds of attacks to learn about other parties' private integer strings without being caught. In this paper, we present these attacks, and propose countermeasures to make the protocol secure again. The improved protocol not only can resist these attacks but also remove the need for the quantum Fourier transform and encoding quantum operations by participants., Comment: 12 pages. Our work has been submitted to Quantum Information Processing on 2 May 2019. A similar work appeared on arXiv (arXiv:1907.02656) on 5 July 2019. One more attack based on entangled states is proposed in our work than in arXiv:1907.02656. Besides, our improved protocol removes the need for the quantum Fourier transform and encoding quantum operations by participants

It is known that quantum scissors, as non-deterministic amplifiers, can enhance the performance of Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) in noisy and long-distance regimes of operation. Here, we extend this result to a non-Gaussian CV-QKD protocol with discrete modulation. We show that, by using a proper setting, the use of quantum scissors in the receiver of such discrete-modulation CV-QKD protocols would allow us to achieve positive secret key rates at high loss and high excess noise regimes of operation, which would have been otherwise impossible. This also keeps the prospect of running discrete-modulation CV-QKD over CV quantum repeaters alive., Comment: 11 pages, 7 figures

We extend the relation between absolutely maximally entangled (AME) states and quantum maximum distance separable (QMDS) codes by constructing whole families of QMDS codes from their parent AME states. We introduce a reduction-friendly form for the generator set of the stabilizer representation of an AME state, from which the stabilizer form for children codes, all QMDS, can be obtained. We then relate this to optimal codes for one-way quantum repeaters, by minimizing the short-term infrastructure cost as well as the long-term running cost of such quantum repeaters. We establish that AME states provide a framework for a class of QMDS codes that can be used in quantum repeaters., Comment: 15 pages, 3 figures

Quantum communication is rapidly gaining popularity due to its high security and technological maturity. However, most implementations are limited to just two communicating parties (users). Quantum communication networks aim to connect a multitude of users. Here we present a fully connected quantum communication network on a city wide scale without active switching or trusted nodes. We demonstrate simultaneous and secure connections between all 28 pairings of 8 users. Our novel network topology is easily scalable to many users, allows traffic management features and minimises the infrastructure as well as the user hardware needed., Comment: 16 pages, 9 figures, 3 tables. Corrected typos, updated references

We present a secure multi-party quantum summation protocol based on quantum teleportation, in which a malicious, but non-collusive, third party (TP) helps compute the summation. In our protocol, TP is in charge of entanglement distribution and Bell states are shared between participants. Users encode the qubits in their hand according to their private bits and perform Bell-state measurements. After obtaining participants' measurement results, TP can figure out the summation. The participants do not need to send their encoded states to others, and the protocol is therefore congenitally free from Trojan horse attacks. In addition, our protocol can be made secure against loss errors, because the entanglement distribution occurs only once at the beginning of our protocol. We show that our protocol is secure against attacks by the participants as well as the outsiders., Comment: 14 pages, 5 figures

We propose a low-complexity near-optimal wavelength allocation technique for quantum key distribution access networks that rely on wavelength division multiple access. Such networks would allow users to send quantum and classical signals simultaneously on the same optical fiber infrastructure. Users can be connected to the access network via optical wireless or wired links. We account for the background noise present in the environment, as well as the Raman noise generated by classical channels, and calculate the secret key generation rate for quantum channels in the finite-key setting. This allows us to examine the feasibility of such systems in realistic scenarios when the secret key exchange needs to be achieved in a limited time scale. Our numerical results show that, by proper choice of system parameters for this noisy system, it is possible to exchange a secret key in tens of seconds. Moreover, our proposed algorithm can enhance the key rate of quantum channels, especially in high noise and/or high loss regimes of operation.

The use of quantum scissors, as candidates for non-deterministic amplifiers, in continuous-variable quantum key distribution systems is investigated. Such devices rely on single-photon sources for their operation and as such, they do not necessarily preserve the Guassianity of the channel. Using exact analytical modeling for system components, we bound the secret key generation rate for the system that uses quantum scissors. We find that for non-zero values of excess noise such a system can reach longer distances than the system with no amplification. The prospect of using quantum scissors in continuous-variable quantum repeaters is therefore emboldened., Comment: 11 pages, 7 figures, 1 table

Using a high-quality GaAs planar microcavity, we optically generate polariton pairs, and verify their correlations by means of time-resolved single-photon detection. We find that correlations between the different modes are consistently lower than identical mode correlations, which is attributed to the presence of uncorrelated background. We discuss a model to quantify the effects of such a background on the observed correlations. Using spectral and temporal filtering, the background can be suppressed and a change in photon statistics towards non-classical correlations is observed. These results improve our understanding of the statistics of polariton-polariton scattering and background mechanisms, and pave the way to the generation of entangled polariton pairs.

Continuous-variable quantum cryptographic systems, including random number generation and key distribution, are often based on coherent detection. The essence of the security analysis lies in the randomness quantification. Previous analyses employ a semi-quantum picture, where the strong local oscillator limit is assumed. Here, we investigate the randomness of homodyne detection in a full quantum scenario by accounting for the shot noise in the local oscillator, which requires us to develop randomness measures in the infinite-dimensional scenario. Similar to the finite-dimensional case, our introduced measure of randomness corresponds to the relative entropy of coherence defined for an infinite-dimensional system. Our results are applicable to general coherent detection systems, in which the local oscillator is inevitably of finite power. As an application example, we employ the analysis method to a practical vacuum-fluctuation quantum random number generator and explore the limits of generation rate given a continuous-wave laser., Comment: 8 pages, 4 figures

Memory-assisted measurement-device-independent quantum key distribution (MA-MDI-QKD) is a promising scheme that aims to improve the rate-versus-distance behavior of a QKD system by using the state-of-the-art devices. It can be seen as a bridge between current QKD links to quantum repeater based networks. While, similar to quantum repeaters, MA-MDI-QKD relies on quantum memory (QM) units, the requirements for such QMs are less demanding than that of probabilistic quantum repeaters. Here, we present a variant of MA-MDI-QKD structure that relies on only a single physical QM: a nitrogen-vacancy center embedded into a cavity where its electronic spin interacts with photons and its nuclear spin is used for storage. This enables us to propose a simple but efficient MA-MDI-QKD scheme resilient to memory errors and capable of beating, in terms of rate and reach, existing QKD demonstrations. We also show how we can extend this setup to a quantum repeater system, reaching, thus, larger distances., Comment: 9 pages, 6 figures

Memory-assisted quantum key distribution (MA-QKD) has recently been proposed as a technique to improve the rate-versus-distance behavior of QKD systems by using existing, or nearly-achievable, quantum technologies. The promise is that MA-QKD would require less demanding quantum memories than the ones needed for probabilistic quantum repeaters. Nevertheless, early investigations suggest that, in order to beat the conventional no-memory QKD schemes, the quantum memories used in the MA-QKD protocols must have high bandwidth-storage products and short interaction times. Among different types of quantum memories, ensemble-based memories offer some of the required specifications, but they typically suffer from multiple excitation effects. To avoid the latter issue, in this paper, we propose two new variants of MA-QKD both relying on single-photon sources (SPSs) for entangling purposes. One is based on known techniques for entanglement distribution in quantum repeaters. This scheme turns out to offer no advantage even if one uses ideal SPSs. By finding the root cause of the problem, we then propose another setup, which can outperform single no-QM setups even if we allow for some imperfections in our SPSs. For such a scheme, we compare the key rate for different types of ensemble-based memories and show that certain classes of atomic ensembles can improve the rate-versus-distance behavior., Comment: 33 pages, 11 figures

We examine the applicability of wireless indoor quantum key distribution (QKD) in hybrid quantum-classical networks. We propose practical configurations that would enable wireless access to such networks. The proposed setups would allow an indoor wireless user, equipped with a QKD-enabled mobile device, to communicate securely with a remote party on the other end of the access network. QKD signals, sent through wireless indoor channels, are combined with classical ones and sent over shared fiber links to the remote user. Dense wavelengthdivision multiplexing would enable the simultaneous transmission of quantum and classical signals over the same fiber. We consider the adverse effects of the background noise induced by Raman scattered light on the QKD receivers due to such an integration. In addition, we consider the loss and the background noise that arise from indoor environments. We consider a number of discrete and continuous-variable QKD protocols and study their performance in different scenarios.

We propose a scheme of loss resilient entanglement swapping between two distant parties in lossy optical fibre. In this scheme, Alice and Bob each begin with a pair of entangled non-classical states; these "hybrid states" of light are entangled discrete variable (Fock state) and continuous variable (coherent state) pairs. The continuous variable halves of each of these pairs are sent through lossy optical fibre to a middle location, where these states are then mixed (using a 50:50 beam-splitter) and measured. The detection scheme we use is to measure one of these modes via vacuum detection, and to measure the other mode using homodyne detection. In this work we show that the Bell state $\lvert\Phi^{+}\rangle=(\lvert 00\rangle+\lvert 11\rangle)/\sqrt{2}$ can theoretically be produced following this scheme with high fidelity and entanglement, even when allowing for a small amount of loss. It can be shown that there is an optimal amplitude value ($\alpha$) of the coherent state when allowing for such loss. We also investigate the realistic circumstance when the loss is not balanced in the propagating modes. We demonstrate that a small amount of loss mismatch does not destroy the overall entanglement, thus demonstrating the physical practicality of this protocol., Comment: 8 pages, 8 figures

Optimal wavelength assignment in dense-wavelength-division-multiplexing (DWDM) systems that integrate both quantum and classical channels is studied. In such systems, weak quantum key distribution (QKD) signals travel alongside intense classical signals on the same fiber, where the former can be masked by the background noise induced by the latter. Here, we investigate how optimal wavelength assignment can mitigate this problem. We consider different DWDM structures and various sources of crosstalk and propose several near-optimal wavelength assignment methods that maximize the total secret key rate of the QKD channels. Our numerical results show that the optimum wavelength assignment pattern is commonly consisted of several interspersed quantum and classical bands. Using our proposed techniques, the total secret key rate of quantum channels can substantially be improved, as compared to conventional assignment methods, in the noise dominated regimes. Alternatively, we can maximize the number of QKD users supported under certain key rate constraints., Comment: 13 pages, 7 figures

The decoy-state scheme is the most widely implemented quantum key distribution protocol in practice. In order to account for the finite-size key effects on the achievable secret key generation rate, a rigorous statistical fluctuation analysis is required. Originally, a heuristic Gaussian-approximation technique was used for this purpose, which, despite of its analytical convenience, was not sufficiently rigorous. The fluctuation analysis has recently been made rigorous by using the Chernoff bound. There is a considerable gap, however, between the key rate bounds obtained from these new techniques and that obtained from the Gaussian assumption. Here, we develop a tighter bound for the decoy-state method, which yields a smaller failure probability. This improvement results in a higher key rate and increases the maximum distance over which secure key exchange is possible. By optimizing the system parameters, our simulation results show that our new method almost closes the gap between the two previously proposed techniques and achieves a similar performance to that of conventional Gaussian approximations., Comment: 34 pages, 5 figures

We propose and study the feasibility of wireless quantum key distribution (QKD) in indoor environments. Such systems are essential in providing wireless access to the developing quantum communications networks. We find a practical regime of operation, where, in the presence of external light sources and loss, secret keys can be exchanged. Our findings identify the trade-off between the acceptable amount of background light and the receiver field of view, where the latter affects the ease of access to the QKD system. In particular, we show that, using a proper setting, we can provide mobility for the QKD users without imposing stringent conditions on beam steering.

Memory-assisted measurement-device-independent quantum key distribution (MA-MDI-QKD) has recently been proposed as a possible intermediate step towards the realization of quantum repeaters. Despite its relaxing some of the requirements on quantum memories, the choice of memory in relation to the layout of the setup and the protocol has a stark effect on our ability to beat existing no-memory systems. Here, we investigate the suitability of nitrogen vacancy (NV) centers, as quantum memories, in MA-MDI-QKD. We particularly show that moderate cavity enhancement is required for NV centers if we want to outperform no-memory QKD systems. Using system parameters mostly achievable by today's state of the art, we then anticipate some total key rate advantage in the distance range between 300 km and 500 km for cavity-enhanced NV centers. Our analysis accounts for major sources of error including the dark current, the channel loss, and the decoherence of the quantum memories.

We propose orthogonal frequency division multiplexing (OFDM), as a spectrally efficient multiplexing technique, for quantum key distribution (QKD) at the core of trustednode quantum networks. Two main schemes are proposed and analyzed in detail, considering system imperfections, specifically, time misalignment issues. It turns out that while multiple service providers can share the network infrastructure using the proposed multiplexing techniques, no gain in the total secret key generation rate is obtained if one uses conventional all-optical passive OFDM decoders. To achieve a linear increase in the key rate with the number of channels, an alternative active setup for OFDM decoding is proposed, which employs an optical switch in addition to conventional passive circuits. We show that by using our proposed decoder the bandwidth utilization is considerably improved as compared to conventional wavelength division multiplexing techniques., Comment: Equation (23) is fixed

The feasibility of trust-free long-haul quantum key distribution (QKD) networks is addressed. We combine measurement-device-independent QKD (MDI-QKD), as an access technology, with a quantum repeater setup, at the core of future quantum communication networks. This will provide a quantum link none of whose intermediary nodes need to be trusted, or, in our terminology, a trust-free QKD link. As the main figure of merit, we calculate the secret key generation rate when a particular probabilistic quantum repeater protocol is in use. We assume the users are equipped with imperfect single photon sources, which can possibly emit two single photons, or laser sources to implement decoy-state techniques. We consider apparatus imperfection, such as quantum efficiency and dark count of photodetectors, path loss of the channel, and writing and reading efficiencies of quantum memories. By optimizing different system parameters, we estimate the maximum distance over which users can share secret keys when a finite number of memories are employed in the repeater setup.

Quantum memories are enabling devices for extending the reach of quantum key distribution (QKD) systems. The required specifications for memories are, however, often considered too demanding for available technologies. One can change this mindset by introducing memory-assisted measurement-device-independent QKD (MDI-QKD), which imposes less stringent conditions on the memory modules. It has been shown that, in the case of {\em fast} single-qubit memories, we can reach rates and distances not attainable by single no-memory QKD links. Single-qubit memories, such as single atoms or ions, have, currently, too slow of an access time to offer an advantage in practice. Here, we relax that assumption, and consider ensemble-based memories, which satisfy the main two requirements of having short access times and large storage-bandwidth products. Our results, however, suggest that the multiple-excitation effects in such memories can be so detrimental that they may wash away the scaling improvement offered by memory-equipped systems. We then propose an alternative setup that can in principle remedy the above problem. As a prelude to our main problem, we also obtain secret key generation rates for MDI-QKD systems that rely on imperfect single-photon sources with nonzero probabilities of emitting two photons.

We propose a repeat-until-success protocol to improve the performance of probabilistic quantum repeaters. Quantum repeaters rely on passive static linear optics elements and photodetectors to perform Bell-state measurements (BSMs). Conventionally, the success rate of these BSMs cannot exceed 50%, which is an impediment for entanglement swapping between distant quantum memories. Every time that a BSM fails, entanglement needs to be re-distributed between the corresponding memories in the repeater link. The key ingredient in our scheme is a repeatable BSM. Although it too relies only on linear optics and photo-detection, it ideally allows us to repeat every BSM until it succeeds. This, in principle, can turn a probabilistic quantum repeater into a deterministic one. Under realistic conditions, where our measurement devices are lossy, our repeatable BSMs may also fail. However, we show that by using additional threshold detectors, we can improve the entanglement generation rate between one and two orders of magnitude as compared to the probabilistic repeater systems that rely on conventional BSMs. This improvement is sufficient to make the performance of probabilistic quantum repeaters comparable with some of existing proposals for deterministic quantum repeaters., Comment: 11 pages, 8 figures

The variational method in a reformulated Hamiltonian formalism of Quantum Electrodynamics is used to derive relativistic wave equations for systems consisting of n fermions and antifermions of various masses. The derived interaction kernels of these equations include one-photon exchange interactions. The equations have the expected Schroedinger non-relativistic limit. Application to some exotic few lepton systems is discussed briefly., Comment: 22 pages

A protocol with the potential of beating the existing distance records for conventional quantum key distribution (QKD) systems is proposed. It borrows ideas from quantum repeaters by using memories in the middle of the link, and that of measurement-device-independent QKD, which only requires optical source equipment at the user's end. For certain fast memories, our scheme allows a higher repetition rate than that of quantum repeaters, thereby requiring lower coherence times. By accounting for various sources of nonideality, such as memory decoherence, dark counts, misalignment errors, and background noise, as well as timing issues with memories, we develop a mathematical framework within which we can compare QKD systems with and without memories. In particular, we show that with the state-of-the-art technology for quantum memories, it is possible to devise memory-assisted QKD systems that, at certain distances of practical interest, outperform current QKD implementations.

We investigate the consequences of space-time being curved on space-based quantum communication protocols. We analyze tasks that require either the exchange of single photons in a certain entanglement distribution protocol or beams of light in a continuous-variable quantum key distribution scheme. We find that gravity affects the propagation of photons, therefore adding additional noise to the channel for the transmission of information. The effects could be measured with current technology., Comment: Ivette Fuentes previously published also as I. Fuentes-Schuller and I. Fuentes-Guridi

Quantum key distribution over probabilistic quantum repeaters is addressed. We compare, under practical assumptions, two such schemes in terms of their secure key generation rates per quantum memory. The two schemes under investigation are the one proposed by Duan et al. in [Nat. 414, 413 (2001)] and that of Sangouard et al. in [Phys. Rev. A 76, 050301 (2007)]. We consider various sources of imperfection in both protocols, such as nonzero double-photon probabilities at the sources, dark counts in detectors, and inefficiencies in the channel, photodetectors and memories. We also consider memory decay and dephasing processes in our analysis. For the latter system, we determine the maximum value of the double-photon probability beyond which secretkey distillation is not possible. We also find the crossover distance beyond which the repeater schemes outperform the non-repeater ones. We finally compare the two protocols in terms of their achievable secret key generation rates at their optimal settings, Comment: 28 pages, 12 figures

Measurement-device-independent quantum key distribution with a finite number of decoy states is analyzed under finite-data-size assumption. By accounting for statistical fluctuations in parameter estimation, we investigate vacuum+weak- and vacuum+two-weak-decoy-state protocols. In each case, we find proper operation regimes, where the performance of our system is comparable to the asymptotic case for which the key size and the number of decoy states approach infinity. Our results show that practical implementations of this scheme can be both secure and efficient., Comment: 18 pages, 4 figures

Practical schemes for measurement-device-independent quantum key distribution using phase and path or time encoding are presented. In addition to immunity to existing loopholes in detection systems, our setup employs simple encoding and decoding modules without relying on polarization maintenance or optical switches. Moreover, by employing a modified sifting technique to handle the dead-time limitations in single-photon detectors, our scheme can be run with only two single-photon detectors. With a phase-postselection technique, a decoy-state variant of our scheme is also proposed, whose key generation rate scales linearly with the channel transmittance., Comment: 30 pages, 5 figures

This paper addresses multi-user quantum key distribution networks, in which any two users can mutually exchange a secret key without trusting any other nodes. The same network also supports conventional classical communications by assigning two different wavelength bands to quantum and classical signals. Time and code division multiple access (CDMA) techniques, within a passive star network, are considered. In the case of CDMA, it turns out that the optimal performance is achieved at a unity code weight. A listen-before-send protocol is then proposed to improve secret key generation rates in this case. Finally, a hybrid setup with wavelength routers and passive optical networks, which can support a large number of users, is considered and analyzed., Comment: 9 pages, 10 figures

A feasible route towards implementing long-distance quantum key distribution (QKD) systems relies on probabilistic schemes for entanglement distribution and swapping as proposed in the work of Duan, Lukin, Cirac, and Zoller (DLCZ) [Nature 414, 413 (2001)]. Here, we calculate the conditional throughput and fidelity of entanglement for DLCZ quantum repeaters, by accounting for the DLCZ self-purification property, in the presence of multiple excitations in the ensemble memories as well as loss and other sources of inefficiency in the channel and measurement modules. We then use our results to find the generation rate of secure key bits for QKD systems that rely on DLCZ quantum repeaters. We compare the key generation rate per logical memory employed in the two cases of with and without a repeater node. We find the cross-over distance beyond which the repeater system outperforms the non-repeater one. That provides us with the optimum inter-node distancing in quantum repeater systems. We also find the optimal excitation probability at which the QKD rate peaks. Such an optimum probability, in most regimes of interest, is insensitive to the total distance., Comment: 12 pages, 6 figures; Fig. 5(a) is replaced