Memory dephasing and its impact on the rate of entanglement generation in quantum repeaters is addressed. For systems that rely on probabilistic schemes for entanglement distribution and connection, we estimate the maximum achievable rate per employed memory for our optimized partial nesting protocol. We show that, for any given distance $L$, the polynomial scaling of rate with distance can only be achieved if quantum memories with coherence times on the order of $L/c$ or longer, with $c$ being the speed of light in the channel, are available. The above rate degrades as a power of $\exp[-\sqrt{(L/c)/ τ_c}]$ with distance when the coherence time $τ_c \ll L/c$.
Quantum repeaters with multiple quantum memories provide high throughput, low latency, and high fidelity quantum state (qubit) transfer over long distances. However, conventional quantum repeater protocols require full connections among the multiple quantum memories in a repeater node, which is technically challenging. Here, we propose a quantum repeater protocol based on backward propagating photon emission and absorption, where the quantum memories are multiplexed in the time-domain to speed up a single transmission channel without requiring full connectivity, drastically facilitating physic…
We study the feasibility of meaningful proof-of-principle demonstrations of several quantum repeater protocols with photon (single-photon and photon-pair) sources and atomic-ensemble based quantum memories. We take into account non-unit memory efficiencies that decay exponentially with time, which complicates the calculation of repeater rates. We discuss implementations based on quantum dots, parametric down-conversion, rare-earth-ion doped crystals, and Rydberg atoms. Our results provide guidance for the near-term implementation of long-distance quantum repeater demonstrations, suggesting tha…
One of the main problems in quantum communications is how to achieve high rates at long distances. Quantum repeaters, i.e., untrusted, intermediate relay stations, are necessary to overcome the repeaterless bound which sets the fundamental rate-distance limit of repeaterless communications. In this work, we introduce a continuous-variable protocol which overcomes the repeaterless bound and scales like the single-repeater bound using just one linear-optical device called a "quantum scissor", combining the entanglement distillation and entanglement swapping elements of previous repeater proposal…
We propose a quantum repeater protocol which builds on the well-known DLCZ protocol [L.M. Duan, M.D. Lukin, J.I. Cirac, and P. Zoller, Nature 414, 413 (2001)], but which uses photon pair sources in combination with memories that allow to store a large number of temporal modes. We suggest to realize such multi-mode memories based on the principle of photon echo, using solids doped with rare-earth ions. The use of multi-mode memories promises a speedup in entanglement generation by several orders of magnitude and a significant reduction in stability requirements compared to the DLCZ protocol.
We present a detailed description of the diagrammatic technique, recently devised in [V. V. Kuzmin et.al., npj Quantum Information 5, 115 (2019)], for semi-analytical description of large-scale quantum-repeater networks. The technique takes into account all essential experimental imperfections, including dissipative Liouville dynamics of the network quantum memories and the classical communication delays. The results obtained with the semi-analytic method match the exact Monte Carlo simulations while the required computational resources scale only linearly with the network size. The presented …
The construction of large-scale quantum networks relies on the development of practical quantum repeaters. Many approaches have been proposed with the goal of outperforming the direct transmission of photons, but most of them are inefficient or difficult to implement with current technology. Here, we present a protocol that uses a semi-hierarchical structure to improve the entanglement distribution rate while reducing the requirement of memory time to a range of tens of milliseconds. This protocol can be implemented with a fixed distance of elementary links and fixed requirements on quantum me…
Inspired by recent developments in the control and manipulation of quantum dot nuclear spins, which allow for the transfer of an electron spin state to the surrounding nuclear-spin ensemble for storage, we propose a quantum repeater scheme that combines individual quantum dot electron spins and nuclear-spin ensembles, which serve as spin-photon interfaces and quantum memories respectively. We consider the use of low-strain quantum dots embedded in high-cooperativity optical microcavities. Quantum dot nuclear-spin ensembles allow for the long-term storage of entangled states, and heralded entan…
We present an exact rate analysis for a secret key that can be shared among two parties employing a linear quantum repeater chain. One of our main motivations is to address the question whether simply placing quantum memories along a quantum communication channel can be beneficial in a realistic setting. The underlying model assumes deterministic entanglement swapping of single-spin quantum memories and it excludes probabilistic entanglement distillation, and thus two-way classical communication, on higher nesting levels. Within this framework, we identify the essential properties of any optim…
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 …
Hybrid Quantum Repeaters with Ensemble-based Quantum Memories and Single-spin Photon Transducers
QuTech, Delft University of Technology（代尔夫特理工大学 QuTech）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Department of Applied Physics, University of Geneva（日内瓦大学应用物理系）；Constructor University（Constructor 大学）；Department of Physics, Harvard University（哈佛大学物理系）
In present-day quantum communications, one of the main problems is the lack of a quantum repeater design that can simultaneously secure high rates and long distances. Recent literature has established the end-to-end capacities that are achievable by the most general protocols for quantum and private communication within a quantum network, encompassing the case of a quantum repeater chain. However, whether or not a physical design exists to approach such capacities remains a challenging objective. Driven by this motivation, in this work, we put forward a design for continuous-variable quantum r…
The quantum repeater protocol is a promising approach to implement long-distance quantum communication and large-scale quantum networks. A key idea of the quantum repeater protocol is to use long-lived quantum memories to achieve efficient entanglement connection between different repeater segments with a polynomial scaling. Here we report an experiment which realizes efficient connection of two quantum repeater segments via on-demand entanglement swapping by the use of two atomic quantum memories with storage time of tens of milliseconds. With the memory enhancement, scaling-changing accelera…
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 at the repeater nodes. Here we show that such a requirement is, in fact, unnecessary by introducing the concept of all photonic quantum repeate…
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…
We generalize measurement-device-independent quantum key distribution [ H.-K. Lo, M. Curty, and B. Qi, Phys. Rev. Lett. 108, 130503 (2012) ] to the scenario where the Bell-state measurement station contains also heralded quantum memories. We find analytical formulas, in terms of device imperfections, for all quantities entering in the secret key rates, i.e., the quantum bit error rate and the repeater rate. We assume either single-photon sources or weak coherent pulse sources plus decoy states. We show that it is possible to significantly outperform the original proposal, even in presence of d…
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 o…
Owing to the inevitable loss in communication channels, the distance of entanglement distribution is limited to approximately 100 kilometres on the ground. Quantum repeaters can circumvent this problem by using quantum memory and entanglement swapping. As the elementary link of a quantum repeater, the heralded distribution of two-party entanglement between two remote nodes has only been realized with built-in-type quantum memories. These schemes suffer from the trade-off between multiplexing capacity and deterministic properties and hence hinder the development of efficient quantum repeaters. …
Quantum repeater segment with free-space coupled co-trapped ions using telecom photon interference
Universität des Saarlandes（萨尔兰大学）；Zentrum für Quantentechnologien (QuTe), Universität des Saarlandes（萨尔兰大学量子技术中心 (QuTe)）；Ruhr-Universität Bochum（波鸿鲁尔大学）
The realization of a functional quantum repeater is one of the major research goals in long-distance quantum communication. Among the different approaches that are being followed, the one relying on quantum memories interfaced with deterministic quantum emitters is considered as among one of the most promising solutions. In this work, we focus on memory-based quantum-repeater schemes that rely on semiconductor quantum dots for the generation of polarization entangled photons. Going through the most relevant figures of merit related to efficiency of the photon source, we select significant deve…
The distribution of quantum states over long distances is limited by photon loss. Straightforward amplification as in classical telecommunications is not an option in quantum communication because of the no-cloning theorem. This problem could be overcome by implementing quantum repeater protocols, which create long-distance entanglement from shorter-distance entanglement via entanglement swapping. Such protocols require the capacity to create entanglement in a heralded fashion, to store it in quantum memories, and to swap it. One attractive general strategy for realizing quantum repeaters is b…
Quantum repeaters - fundamental building blocks for long-distance quantum communication - are based on the interaction between photons and quantum memories. The photons must fulfil stringent requirements on central frequency, spectral bandwidth and purity in order for this interaction to be efficient. We present a design scheme for monolithically integrated resonant photon-pair sources based on parametric down-conversion in nonlinear waveguides, which facilitate the generation of such photons. We investigate the impact of different design parameters on the performance of our source. The genera…
Conventional wisdom suggests that realistic quantum repeaters will require quasi-deterministic sources of entangled photon pairs. In contrast, we here study a quantum repeater architecture that uses simple parametric down-conversion sources, as well as frequency-multiplexed multimode quantum memories and photon-number resolving detectors. We show that this approach can significantly extend quantum communication distances compared to direct transmission. This shows that important trade-offs are possible between the different components of quantum repeater architectures.
Overcoming repeaterless bounds for the secret key rate capacity of quantum key distribution protocols is still a challenge with current technology. D. Luong et al. [Applied Physics B 122, 96 (2016)] proposed a protocol to beat a repeaterless bound using one pair of quantum memories. However, the required experimental parameters for the memories are quite demanding. We extend the protocol with multiple pairs of memories, operated in a parallel manner to relax these conditions. We quantify the amount of relaxation in terms of the most crucial memory parameters, given the number of applied memory…
A global quantum repeater network involving satellite-based links is likely to have advantages over fiber-based networks in terms of long-distance communication, since the photon losses in free space scale only polynomially with the distance -- compared to the exponential losses in optical fibers. To simulate the performance of such networks, we have introduced a scheme of large-scale event-based Monte Carlo simulation of quantum repeaters with multiple memories that can faithfully represent loss and imperfections in these memories. In this work, we identify the quantum key distribution rates …
Scalable entanglement distribution using encoded hybrid repeater chains
University of Texas at Arlington（阿灵顿得克萨斯大学）；Manning College of Information and Computer Sciences, University of Massachusetts Amherst（马萨诸塞大学阿姆赫斯特分校曼宁信息学与计算机科学学院）；Department of Electrical and Computer Engineering, University of Maryland College Park（马里兰大学帕克分校电气与计算机工程系）
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…
We propose a realistic protocol to generate entanglement between quantum memories at neighboring nodes in hybrid quantum repeaters. Generated entanglement includes only one type of error, which enables efficient entanglement distillation. In contrast to the known protocols with such a property, our protocol with ideal detectors achieves the theoretical limit of the success probability and the fidelity to a Bell state, promising higher efficiencies in the repeaters. We also show that the advantage of our protocol remains even with realistic threshold detectors.
We study entanglement creation over global distances based on a quantum repeater architecture that uses low-earth orbit satellites equipped with entangled photon sources, as well as ground stations equipped with quantum non-demolition detectors and quantum memories. We show that this approach allows entanglement creation at viable rates over distances that are inaccessible via direct transmission through optical fibers or even from very distant satellites.
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…
Quantum repeaters have been proposed as a way of extending the reach of quantum communication. First generation approaches use entanglement swapping to connect entangled links along a long distance channel. Recently, there have been proposals for first generation quantum repeaters for continuous variables. In this paper, we present an improved continuous variable repeater scheme using optimal Gaussian entanglement swapping. Our scheme uses the noiseless linear amplifier for entanglement distillation. We show that with the simplest configuration of the noiseless linear amplifier and under the a…
Using 2 km of standard telecom optical fibres, we teleport qubits carried by photons of 1310 nm wavelength to qubits in another lab carried by a photons of 1550 nm wavelength. The photons to be teleported and the necessary entangled photon pairs are created in two different non-linear crystals. The measured mean fidelity is of 81.2 %. We discuss how this could be used as quantum repeaters without quantum memories.
We present the analysis of behavior of N identical finite time memories with the imperfections characterized by a step-function model, based on a study of independent copies of the geometric distribution. We show a step-by-step derivation of a formula for the average waiting time for obtaining N successes within a given time span τ, which was used recently in the analysis of quantum repeater rates.
Networked entanglement is an essential component for a plethora of quantum computation and communication protocols. Direct transmission of quantum signals over long distances is prevented by fibre attenuation and the no-cloning theorem, motivating the development of quantum repeaters, designed to purify entanglement, extending its range. Quantum repeaters have been demonstrated over short distances, but error-corrected, global repeater networks with high bandwidth require new technology. Here we show that error corrected quantum memories installed in cargo containers and carried by ship can pr…
Quantum information degrades over distance due to the unavoidable imperfections of the transmission channels, with loss as the leading factor. This simple fact hinders quantum communication, as it relies on propagating quantum systems. A solution to this issue is to introduce quantum repeaters at regular intervals along a lossy channel, to revive the quantum signal. In this work we study unitary one-way quantum repeaters, which do not need to perform measurements and do not require quantum memories, and are therefore considerably simpler than other schemes. We introduce and analyze two methods…
Quantum communication is a method that offers efficient and secure ways for the exchange of information in a network. Large-scale quantum communication (of the order of 100 km) has been achieved; however, serious problems occur beyond this distance scale, mainly due to inevitable photon loss in the transmission channel. Quantum communication eventually fails when the probability of a dark count in the photon detectors becomes comparable to the probability that a photon is correctly detected. To overcome this problem, Briegel, Dür, Cirac and Zoller (BDCZ) introduced the concept of quantum repea…
In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity. The scheme tolerates general errors on the percent level.
Recently, Briegel et al. present a quantum repeaters protocol using nest entanglement purification for long distance quantum communication(Physical Review Letters \textbf{81},5932). In this paper we present a modified scheme for constructing an optimal quantum repeater using doubly entangled photon pairs that overcomes the limitations of quantum communication via noisy channels. Based on the imperfect quantum operations and classical communications, the polarization entangled quantum channels can be built with a better efficiency.
We present a detailed rate analysis for a hybrid quantum repeater assuming perfect memories and using optimal probabilistic entanglement generation and deterministic swapping routines. The hybrid quantum repeater protocol is based on atomic qubit-entanglement distribution through optical coherent-state communication. An exact, analytical formula for the rates of entanglement generation in quantum repeaters is derived, including a study on the impacts of entanglement purification and multiplexing strategies. More specifically, we consider scenarios with as little purification as possible and we…
Quantum repeaters are indispensable tools for long-distance quantum communication. However, frequency matching between entangled photon sources and remote quantum memories (QMs) is difficult, which is an obstacle to the implementation of quantum repeaters. In this paper, we demonstrate a method to achieve the coupling of a Pr:YSO as a fixed-time QM with a single telecommunication-wavelength photon through frequency stabilization using an optical frequency comb over all applied laser wavelengths. The demonstrated method can lead to the implementation of a quantum repeater scheme enabling an imp…
Global scale quantum communication links will form the backbone of the quantum internet. However, exponential loss in optical fibres precludes any realistic application beyond few hundred kilometres. Quantum repeaters and space-based systems offer to overcome this limitation. Here, we analyse the use of quantum memory (QM)-equipped satellites for quantum communication focussing on global range repeaters and Measurement-Device-Independent (MDI) QKD. We demonstrate that satellites equipped with QMs provide three orders of magnitude faster entanglement distribution rates than existing protocols b…
The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of both the ultimate capacities of quantum channels and the efficiency of imperfect quantum repeaters. In this work, using a recently developed node-splitting technique which introduces internal losses and noise into repeater devices, we present achievable end-to-end rates for noisy-repeater quantum networks. These are obtained by extending the coherent and re…
A Metropolitan-scale Multiplexed Quantum Repeater with Bell Nonlocality
University of Science and Technology of China（中国科学技术大学）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（中国科学技术大学安徽省量子网络重点实验室）；CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学中国科学院量子信息与量子物理前沿卓越中心）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
