Long Distance Quantum Key Distribution without Quantum Memory

Memory-assisted long-distance phase-matching quantum key distribution

We propose a scheme that generalizes the loss scaling properties of twin-field or phase-matching quantum key distribution (QKD) related to a channel of transmission $η_{total}$ from $\sqrt{η_{total}}$ to $\sqrt[2n]{η_{total}}$ by employing n-1 memory stations with spin qubits and n beam-splitter stations including optical detectors. Our scheme's resource states are similar to the coherent-state-based light-matter entangled states of a previous hybrid quantum repeater, but unlike the latter our scheme avoids the necessity of employing 2n-1 memory stations and writing the transmitted optical sta…

Memory-Assisted Quantum Key Distribution with a Single Nitrogen Vacancy Center

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 ce…

Memory-assisted measurement-device-independent quantum key distribution

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 back…

Long-distance quantum communication over noisy networks without long-time quantum memory

The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension $D$ and transmission of quantum information in a $D+1$-dimensional network. We show that it is possible to obtain long-distance entanglement in a noisy two-dimensional (2D) netw…

Memory Imperfections in Atomic Ensemble-based Quantum Repeaters

Quantum repeaters promise to deliver long-distance entanglement overcoming noise and loss in realistic quantum channels. A promising class of repeaters, based on atomic ensemble quantum memories and linear optics, follow the proposal by Duan et al [Nature 414, 413, 2001]. Here we analyse this protocol in terms of a very general model for the quantum memories employed. We derive analytical expressions for scaling of entanglement with memory imperfections, dark counts, loss and distance, and apply our results to two specific quantum memory protocols. Our methods apply to any quantum memory with …

Device independent quantum key distribution secure against coherent attacks with memoryless measurement devices

Device independent quantum key distribution aims to provide a higher degree of security than traditional QKD schemes by reducing the number of assumptions that need to be made about the physical devices used. The previous proof of security by Pironio et al. applies only to collective attacks where the state is identical and independent and the measurement devices operate identically for each trial in the protocol. We extend this result to a more general class of attacks where the state is arbitrary and the measurement devices have no memory. We accomplish this by a reduction of arbitrary adver…

无量子存储器的抗集体攻击受控量子密钥协商协议

Collective attack free controlled quantum key agreement without quantum memory

该研究提出无需量子存储器的受控量子密钥协商协议，通过安全证明验证其抗假冒欺诈与集体攻击能力，对比现有方案体现出效率优势与资源简化的贡献。

On the role of memory errors in quantum repeaters

We investigate the influence of memory errors in the quantum repeater scheme for long-range quantum communication. We show that the communication distance is limited in standard operation mode due to memory errors resulting from unavoidable waiting times for classical signals. We show how to overcome these limitations by (i) improving local memory, and (ii) introducing two new operational modes of the quantum repeater. In both operational modes, the repeater is run blindly, i.e. without waiting for classical signals to arrive. In the first scheme, entanglement purification protocols based on o…

Memory effects in quantum channel discrimination

We consider quantum-memory assisted protocols for discriminating quantum channels. We show that for optimal discrimination of memory channels, memory assisted protocols are needed. This leads to a new notion of distance for channels with memory. For optimal discrimination and estimation of sets of unitary channels memory-assisted protocols are not required.

Device-independent quantum key distribution secure against adversaries with no long-term quantum memory

Device-Independent Quantum Key Distribution (DIQKD) is a formalism that supersedes traditional quantum key distribution, as its security does not rely on any detailed modelling of the internal working of the devices. This strong form of security is possible only using devices producing correlations that violate a Bell inequality. Full security proofs of DIQKD have been recently reported, but they tolerate zero or small amounts of noise and are restricted to protocols based on specific Bell inequalities. Here, we provide a security proof of DIQKD that is both more efficient and noise resistant,…

Long-Distance Continuous-Variable Quantum Key Distribution over 202.81 km of Fiber

Quantum key distribution provides secure keys resistant to code-breaking quantum computers. The continuous-variable version of quantum key distribution offers the advantages of higher secret key rates in metropolitan areas, as well as the use of standard telecom components that can operate at room temperature. However, the transmission distance of these systems (compared with discrete-variable systems) are currently limited and considered unsuitable for long-distance distribution. Herein, we report the experimental results of long distance continuous-variable quantum key distribution over 202.…

基于单光子源的高效长距离量子存储辅助设备无关量子秘密共享

High-efficiency and long-distance quantum memory-assisted device-independent quantum secret sharing with single photon sources

针对设备无关量子秘密共享距离短、效率低的问题，提出基于单光子源和量子存储辅助的协议，利用heralded架构实现理论无限传输距离，密钥效率提升六至七个数量级。

Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation

We present a continuous-variable quantum key distribution protocol combining a discrete modulation and reverse reconciliation. This protocol is proven unconditionally secure and allows the distribution of secret keys over long distances, thanks to a reverse reconciliation scheme efficient at very low signal-to-noise ratio.

使用多模量子存储器实现测量设备无关量子密钥分发的非线性提升

Nonlinear improvement of measurement-device-independent quantum key distribution using multimode quantum memory

本研究提出基于量子存储器按需存储与多模存储功能的MDI-QKD方案，实现安全密钥率非线性提升，采用原子频率梳构建可行架构，可扩展至量子中继器并为模式数提升提供实验依据。

Memory-assisted quantum key distribution resilient against multiple-excitation effects

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 qu…

具有自适应 syndrome 识别的内存校正量子中继器

Memory-corrected quantum repeaters with adaptive syndrome identification

该研究通过引入校验矩阵模型分析编码量子存储器对中小型量子中继器密钥率的影响，发现5量子比特码和Steane码性能更优，能提升存储器相干时间并降低资源开销，使内存校正中继器在未编码中继器失效的参数下生成密钥且速率更高。

Long-distance quantum key distribution based on the physical loss control

Existing quantum cryptography is resistant against secrecy-breaking quantum computers but suffers fast decay of the signal at long distances. The various types of repeaters of propagating quantum states have been developed to meet the challenge, but the problem is far from being solved. We step in the breach and put forth long-distance high secrecy optical cryptography, creating the fast quantum key distribution over distances up to 40,000 kilometers. The key element of the proposed protocol is the physical control over the transmission line.

Robust creation of entanglement between remote memory qubits

In this Letter we propose a robust quantum repeater architecture building on the original DLCZ protocol [L.M. Duan \textit{et al.}, Nature \textbf{414}, 413 (2001)]. The architecture is based on two-photon Hong-Ou-Mandel-type interference which relaxes the long distance stability requirements by about 7 orders of magnitude, from sub wavelength for the single photon interference required by DLCZ to the coherence length of the photons. Our proposal provides an exciting possibility for robust and realistic long distance quantum communication.

Measurement-device-independent quantum key distribution with nitrogen vacancy centers in diamond

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 wa…

Entanglement distribution between quantum repeater nodes with an absorptive type memory

Quantum repeaters, which are indispensable for long-distance quantum communication, are necessary for extending the entanglement from short distance to long distance; however, high-rate entanglement distribution, even between adjacent repeater nodes, has not been realized. In a recent work by C. Jones, et al., New J. Phys. 18, 083015 (2016), the entanglement distribution rate between adjacent repeater nodes was calculated for a plurality of quantum dots, nitrogen-vacancy centers in diamond, and trapped ions adopted as quantum memories inside the repeater nodes. Considering practical use, arran…

Practical quantum key distribution over 60 hours at an optical fiber distance of 20km using weak and vacuum decoy pulses for enhanced security

Experimental one-way decoy pulse quantum key distribution running continuously for 60 hours is demonstrated over a fiber distance of 20km. We employ a decoy protocol which involves one weak decoy pulse and a vacuum pulse. The obtained secret key rate is on average over 10kbps. This is the highest rate reported using this decoy protocol over this fiber distance and duration.

Long-distance continuous-variable quantum key distribution with efficient channel estimation

We investigate the main limitations which prevent the continuous-variable quantum key distribution protocols from achieving long distances in the finite-size setting. We propose a double-modulation protocol which allows using each state for both channel estimation and key distribution. As opposed to the standard method, we optimize the parameters of the protocol and consider squeezed as well as coherent states as a signal. By optimally combining the resources the key rate can approach the theoretical limit for long distances, and one can obtain about ten times higher key rate using ten times s…

无序多体疤痕系统中记忆辅助的态转移优势

Memory-assisted advantage for state transfer in disordered quantum many-body scar system

研究无序记忆效应如何促进多体疤痕系统中的量子态转移，发现记忆性无序相比无记忆无序能显著提升转移保真度，且疤痕度与保真度正相关。

Long-distance practical quantum key distribution by entanglement swapping

We develop a model for practical, entanglement-based long-distance quantum key distribution employing entanglement swapping as a key building block. Relying only on existing off-the-shelf technology, we show how to optimize resources so as to maximize secret key distribution rates. The tools comprise lossy transmission links, such as telecom optical fibers or free space, parametric down-conversion sources of entangled photon pairs, and threshold detectors that are inefficient and have dark counts. Our analysis provides the optimal trade-off between detector efficiency and dark counts, which ar…

Photon-Echo Quantum Memory

The future of long-distance quantum communication relies on the availability of quantum memory, i.e. devices that allow temporal storage of quantum information. We review research related to quantum state storage based on a photon-echo approach in rare earth ion doped crystals and glasses.

Quantum distance-based classifier with constant size memory, distributed knowledge and state recycling

In this work we examine recently proposed distance-based classification method designed for near-term quantum processing units with limited resources. We further study possibilities to reduce the quantum resources without any efficiency decrease. We show that only a part of the information undergoes coherent evolution and this fact allows us to introduce an algorithm with significantly reduced quantum memory size. Additionally, considering only partial information at a time, we propose a classification protocol with information distributed among a number of agents. Finally, we show that the in…

Quantum teleportation from a telecom-wavelength photon to a solid-state quantum memory

In quantum teleportation, the state of a single quantum system is disembodied into classical information and purely quantum correlations, to be later reconstructed onto a second system that has never directly interacted with the first one. This counterintuitive phenomenon is a cornerstone of quantum information science due to its essential role in several important tasks such as the long-distance transmission of quantum information using quantum repeaters. In this context, a challenge of paramount importance is the distribution of entanglement between remote nodes, and to use this entanglement…

寻找并突破连续变量量子密钥分发的现实速率-距离极限

Finding and breaking the realistic rate-distance limit of continuous variable quantum key distribution

本文研究连续变量量子密钥分发的速率-距离极限，揭示Bob端过量噪声及其计算方法的限制作用，并提出基于纯过量噪声的密钥率计算方法以突破现实极限。

Dead-time optimization to increase secure distance range in prepare and measure quantum key distribution protocols

Afterpulsing is a factor limiting the distance over which discrete-variable quantum key distribution systems are secure, and a common feature in single-photon detectors. The relevance of this phenomenon stems from its stochastic, self-interacting nature and the fact that its rate rises with the number of avalanche events, which increases the quantum bit error rate. Here we introduce an effective analytic model, including dead-time and afterpulsing corrections, where afterpulsing correction depends on dead-time value. This model is useful to evaluate the performance of prepare and measure quant…

Improved Four-state Continuous-variable Quantum Key Distribution with Long Secure Distance

The four-state continuous-variable quantum key distribution (CVQKD) protocol has a long practical secure distance \cite{Leverrier_PRL_2009}, while it has the difficulty of parameter estimation. We propose an improved four-state protocol, where the covariance matrix can be estimated from experimental data without using the linear channel assumption, and thus ensuring its unconditional security in the asymptotical limit. Our new scheme keeps the advantages of high reconciliation efficiency and long secure distance of the four-state protocol, and it can be implemented under current technology.

High Efficient Secret Key Distillation for Long Distance Continuous Variable Quantum Key Distribution

The continuous variable quantum key distribution is expected to provide high secret key rate without single photon source and detector, but the lack of the secure and effective key distillation method makes it unpractical. Here, we present a secure single-bit-reverse-reconciliation protocol combined with secret information concentration and post-selection, which can distill the secret key with high efficiency and low computational complexity. The simulation results show that this protocol can provide high secret key rate even when the transmission fiber is longer than 150km, which may make the…

Practical long-distance quantum key distribution through concatenated entanglement swapping with parametric down-conversion sources

We develop a theory for long-distance quantum key distribution based on concatenated entanglement swapping using parametric down-conversion sources and show numerical results of our model. The model incorporates practical resources including multi-pair sources, inefficient detectors with dark counts and lossy channels. We calculate the maximum secret key-generation ratefor up to three entanglement swapping stations by optimizing over resource parameters, and our numerical simulation shows that the range of quantum key distribution can in principle be markedly increased but at the expense of an…

Picture-perfect Quantum Key Distribution

We provide a new way to bound the security of quantum key distribution using only two high-level, diagrammatic features of quantum processes: the compositional behavior of complementary measurements and the essential uniqueness of purification. We begin by demonstrating a proof in the simplest case, where the eavesdropper doesn't noticeably disturb the channel at all and has no quantum memory. We then show how this approach extends straightforwardly to account for an eavesdropper with quantum memory and the presence of noise.

Long-distance quantum key distribution using concatenated entanglement swapping with practical resources

We present our approach for sharing photons and assessing resultant four-photon visibility between two distant parties using concatenated entanglement swapping. In addition we determine the corresponding key generation rate and the quantum bit-error rate. Our model is based on practical limitations of resources, including multipair parametric down-conversion sources, inefficient detectors with dark counts and lossy channels. Through this approach, we have found that a trade-off is needed between experimental run-time, pair-production rate and detector efficiency. Concatenated entanglement swap…

Long distance quantum key distribution with continuous variables

We present a continuous-variable quantum key distribution protocol combining a continuous but slightly non-Gaussian modulation together with a efficient reverse reconciliation scheme. We establish the security of this protocol against collective attacks which correspond to a linear quantum channel. In particular, all Gaussian attacks are considered in our framework. We show that this protocol outperforms all known practical protocols, even taking into account finite size effects.

Entanglement Swapping for Repeater Chains with Finite Memory Sizes

We develop entanglement swapping protocols and memory allocation methods for quantum repeater chains. Unlike most of the existing studies, the memory size of each quantum repeater in this work is a parameter that can be optimized. Based on Markov chain modeling of the entanglement distribution process, we determine the trade-off between the entanglement distribution rate and the memory size for temporal multiplexing techniques. We then propose three memory allocation methods that achieve entanglement distribution rates decaying polynomially with respect to the distance while using constant ave…

Entanglement distribution with wavevector-multiplexed quantum memory

Feasible distribution of quantum entanglement over long distances remains a fundamental step towards quantum secure communication and quantum network implementations. Quantum repeater nodes based on quantum memories promise to overcome exponential signal decay inherent to optical implementations of quantum communication. While performance of current quantum memories hinders their practical application, multimode solutions with multiplexing can offer tremendous increase in entanglement distribution rates. We propose to use a wavevector-multiplexed atomic quantum memory (WV-MUX-QM) as a fundamen…

Static memory materials

We simulate static memory materials on a two-dimensional lattice. The bulk properties of such materials depend on boundary conditions. Considerable information can be stored in various local patterns. We observe local probabilities oscillating with the distance from the boundary. The dependence of the local statistical information on this distance can be described by a linear evolution of classical wave functions, including the superposition principle and classical interference. We speculate that these new phenomena could open new algorithmic possibilities analogous to quantum computing.

打破无量子存储条件下量子会议密钥协商的普适限制

Breaking universal limitations on quantum conference key agreement without quantum memory

本文提出一种测量设备无关的量子会议密钥协商协议，利用空间复用和自适应操作突破无量子存储条件下的密钥率界限，在密钥率和传输距离上优于现有方案，并验证了其可组合安全性与有限码长下的实用性。

有限随机砖块电路中的初始状态记忆

Initial State Memory in Finite Random Brickwork Circuits

研究有限随机砖块电路在何种条件下能保留初始状态的局部信息，通过计算演化后子系统缩减态的平均弗罗贝尼乌斯距离，发现当环境子系统小于系统一半时信息保留，否则丢失，并发现大规模下距离趋于普适形式，引入弱边界耗散可观察记忆保持与信息丢失相变。

One-hour coherent optical storage in an atomic frequency comb memory

Photon loss in optical fibers prevents long-distance distribution of quantum information on the ground. Quantum repeater is proposed to overcome this problem, but the communication distance is still limited so far because of the system complexity of the quantum repeater scheme. Alternative solutions include transportable quantum memory and quantum-memory-equipped satellites, where long-lived optical quantum memories are the key components to realize global quantum communication. However, the longest storage time of the optical memories demonstrated so far is approximately 1 minute. Here, by em…

Spatial Multiplexing in a Cavity-Enhanced Quantum Memory

We present a multiplexed quantum repeater protocol based on an ensemble of laser-cooled and trapped rubidium atoms inside an optical ring cavity. We have already demonstrated strong collective coupling in such a system and have constructed a multiplexing apparatus based on a two-dimensional acousto-optical deflector. Here, we show how this system could enable a multiplexed quantum repeater using collective excitations with non-trivial spatial phase profiles (spinwaves). Calculated entanglement generation rates over long distances reveal that such a multiplexed ensemble-cavity platform is a pro…

线性量子存储器中的不可克隆密码学

Unclonable Cryptography in Linear Quantum Memory

研究一次性签名等量子签名令牌，此前相关协议量子存储器需求大，本文开发新技术，显著减小量子密钥大小，在某些情况达渐近最优，为不可克隆密码学发展助力。

Towards highly multimode optical quantum memory for quantum repeaters

Long-distance quantum communication through optical fibers is currently limited to a few hundreds of kilometres due to fiber losses. Quantum repeaters could extend this limit to continental distances. Most approaches to quantum repeaters require highly multimode quantum memories in order to reach high communication rates. The atomic frequency comb memory scheme can in principle achieve high temporal multimode storage, without sacrificing memory efficiency. However, previous demonstrations have been hampered by the difficulty of creating high-resolution atomic combs, which reduces the efficienc…

不完美保真度和量子存储条件下的纠缠分发协议

Entanglement distribution protocols under imperfect fidelity and quantum memory conditions

本文提出一种考虑保真度和不完美存储的本地宣告分发（LHD）协议，通过缩短执行时间提高链路成功概率，在性能上优于现有协议。

Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices

A bipartite quantum interaction corresponds to the most general quantum interaction that can occur between two quantum systems in the presence of a bath. In this work, we determine bounds on the capacities of bipartite interactions for entanglement generation and secret key agreement between two quantum systems. Our upper bound on the entanglement generation capacity of a bipartite quantum interaction is given by a quantity called the bidirectional max-Rains information. Our upper bound on the secret-key-agreement capacity of a bipartite quantum interaction is given by a related quantity calle…

Distillation of secret key from a class of compound memoryless quantum sources

We consider secret-key distillation from tripartite compound classical-quantum-quantum (cqq) sources with free forward public communication under strong security criterion. We design protocols which are universally reliable and secure in this scenario. These are shown to achieve asymptotically optimal rates as long as a certain regularity condition is fulfilled by the the set of its generating density matrices. We derive a multi-letter formula which describes the optimal forward secret-key capacity for all compound cqq sources being regular in this sense. We also determine the forward secret-k…

非阿贝尔自纠正量子记忆与超越n^{1/3}距离障碍的横向非克莱弗门

Non-Abelian Self-Correcting Quantum Memory and Transversal Non-Clifford Gate beyond the $n^{1/3}$ Distance Barrier

本研究提出了一种非阿贝尔自纠正量子记忆，通过非泡利稳定器码和高维杯积实现超越传统距离障碍的拓扑量子计算

Long Distance Continuous-Variable Quantum Key Distribution with a Gaussian Modulation

We designed high-efficiency error correcting codes allowing to extract an errorless secret key in a continuous-variable quantum key distribution protocol using a Gaussian modulation of coherent states and a homodyne detection. These codes are available for a wide range of signal-to-noise ratios on an AWGN channel with a binary modulation and can be combined with a multidimensional reconciliation method proven secure against arbitrary collective attacks. This improved reconciliation procedure considerably extends the secure range of a continuous-variable quantum key distribution with a Gaussian…