Repeater Protocol Research Articles

Asynchronous quantum repeater using multiple quantum memory.

A full-fledged quantum network relies on the formation of entangled links between remote location with the help of quantum repeaters. The famous Duan-Lukin-Cirac-Zoller quantum repeater protocol is based on long distance single-photon interference, which not only requires high phase stability but also cannot generate maximally entangled state. Here, we propose a quantum repeater protocol using the idea of post-matching, which retains the same efficiency as the single-photon interference protocol, reduces the phase-stability requirement and can generate maximally entangled state in principle. We also outline an implementation of our scheme based on the Kerr nonlinear resonator. Numerical simulations show that our protocol has its superiority by comparing with existing protocols under a generic noise model and show the feasibility of building a large-scale quantum communication network with our scheme. We believe our work represents a crucial step towards the construction of a fully-connected quantum network.

Large teleportation of two-qubit state between non-neighboring nodes based on the utilization of multiple cluster states within quantum networks

The transmission of quantum states over extended distances is constrained by photon losses, ruling out direct amplification akin to classical telecommunications due to the non-cloning theorem. Overcoming this challenge involves implementing quantum repeater protocols that leverage entanglement swapping to create long-distance entanglement from shorter distances. A novel multi-hop quantum teleportation scheme, blending concepts from quantum repeaters and teleportation, is under exploration. It aims to transfer arbitrary two-qubit states between two distant parties, even in the absence of a direct quantum channel. Intermediate nodes, connected via a four-qubit entangled cluster state as quantum channels, are introduced based on a more general routing protocol. Bell measurements are independently conducted by the source node (Alice) and all intermediate nodes, with simultaneous transmission of measurement results, significantly reducing time consumption. Determining the quantum state from Bell measurement results requires only the destination node (Bob) for a simple unitary transformation. Moreover, this protocol holds promise for implementation on the IBM Quantum Experience platform once the requisite quantum circuits are designed. This overview encompasses both the theoretical and simulated status of the proposed scheme, with simulated findings incorporated into quantum state tomography to verify the accuracy of the transmitted quantum state.

Faithfully Simulating Near-Term Quantum Repeaters

Quantum repeaters have long been established to be essential for distributing entanglement over long distances. Consequently, their experimental realization constitutes a core challenge of quantum communication. However, there are numerous open questions about implementation details for realistic near-term experimental setups. In order to assess the performance of realistic repeater protocols, here we present , a comprehensive Monte Carlo–based ulation platform for antum peaters that faithfully includes loss and models a wide range of imperfections such as memories with time-dependent noise. Our platform allows us to perform an analysis for quantum repeater setups and strategies that go far beyond known analytical results: This refers to being able to both capture more realistic noise models and analyze more complex repeater strategies. We present a number of findings centered around the combination of strategies for improving performance, such as entanglement purification and the use of multiple repeater stations, and demonstrate that there exist complex relationships between them. We stress that numerical tools such as ours are essential to model complex quantum communication protocols aimed at contributing to the quantum Internet. Published by the American Physical Society 2024

Gate‐Based Protocol Simulations for Quantum Repeaters using Quantum‐Dot Molecules in Switchable Electric Fields

AbstractElectrically controllable quantum‐dot molecules (QDMs) are a promising platform for deterministic entanglement generation and, as such, a resource for quantum‐repeater networks. A microscopic open‐quantum‐systems approach based on a time‐dependent Bloch–Redfield equation is developed to model the generation of entangled spin states with high fidelity. The state preparation is a crucial step in a protocol for deterministic entangled‐photon‐pair generation that is proposed for quantum repeater applications. The theory takes into account the quantum‐dot molecules' electronic properties that are controlled by time‐dependent electric fields as well as dissipation due to electron–phonon interaction. The transition between adiabatic and non‐adiabatic regimes is quantified, which provides insights into the dynamics of adiabatic control of QDM charge states in the presence of dissipative processes. From this, the maximum speed of entangled‐state preparation is inferred under different experimental conditions, which serves as a first step toward simulation of attainable entangled photon‐pair generation rates. The developed formalism opens the possibility for device‐realistic descriptions of repeater protocol implementations.

‘Sawfish’ Photonic Crystal Cavity for Near‐Unity Emitter‐to‐Fiber Interfacing in Quantum Network Applications

AbstractPhoton loss is one of the key challenges to overcome in complex photonic quantum applications. Photon collection efficiencies directly impact the amount of resources required for measurement‐based quantum computation and communication networks. Promising resources include solid‐state quantum light sources. However, efficiently coupling light from a single quantum emitter to a guided mode remains demanding. In this work, photon losses are eliminated by maximizing coupling efficiencies in an emitter‐to‐fiber interface. A waveguide‐integrated ‘Sawfish’ photonic crystal cavity is developed and finite element (FEM) simulations are employed to demonstrate that such an emitter‐to‐fiber interface transfers, with 97.4 % efficiency, the zero‐phonon line (ZPL) emission of a negatively‐charged tin vacancy center in diamond (SnV−) adiabatically to a single‐mode fiber. A surrogate model trained by machine learning provides quantitative estimates of sensitivities to fabrication tolerances. The corrugation‐based Sawfish design proves robust under state‐of‐the‐art nanofabrication parameters, maintaining an emitter‐to‐fiber coupling efficiency of 88.6 %. Applying the Sawfish cavity to a recent one‐way quantum repeater protocol substantiates its potential in reducing resource requirements in quantum communication.

All-photonic one-way quantum repeaters with measurement-based error correction

Quantum repeater is the key technology enabler for long-distance quantum communication. To date, most of the existing quantum repeater protocols are designed based on specific quantum codes or graph states. In this paper, we propose a general framework for all-photonic one-way quantum repeaters based on the measurement-based error correction, which can be adapted to any Calderbank–Shor–Steane code including the recently discovered quantum low-density parity check (QLDPC) codes. We present a decoding scheme, where the error correction process is carried out at the destination based on the accumulated data from the measurements made across the network. This procedure not only outperforms the conventional protocols with independent repeaters but also simplifies the local quantum operations at repeaters. As an example, we numerically show that the [[48, 6, 8]] generalized bicycle code (as a small but efficient QLDPC code) has an equally good performance while reducing the resources by at least an order of magnitude.

Requirements for a processing-node quantum repeater on a real-world fiber grid

We numerically study the distribution of entanglement between the Dutch cities of Delft and Eindhoven realized with a processing-node quantum repeater and determine minimal hardware requirements for verifiable blind quantum computation using color centers and trapped ions. Our results are obtained considering restrictions imposed by a real-world fiber grid and using detailed hardware-specific models. By comparing our results to those we would obtain in idealized settings, we show that simplifications lead to a distorted picture of hardware demands, particularly on memory coherence and photon collection. We develop general machinery suitable for studying arbitrary processing-node repeater chains using NetSquid, a discrete-event simulator for quantum networks. This enables us to include time-dependent noise models and simulate repeater protocols with cut-offs, including the required classical control communication. We find minimal hardware requirements by solving an optimization problem using genetic algorithms on a high-performance-computing cluster. Our work provides guidance for further experimental progress, and showcases limitations of studying quantum-repeater requirements in idealized situations.

Decoherence of Single‐Excitation Entanglement over Duan‐Lukin‐Cirac‐Zoller Quantum Networks Caused by Slow‐Magnetic‐Field Fluctuations and Protection Approach

AbstractAtomic spin‐wave (SW) memory is a building block for quantum repeater. However, due to decoherence caused by atomic motions and magnetic‐field gradients, SW retrieval efficiency decays with storage time. Slow magnetic‐field fluctuations (SMFFs) lead to shot‐to‐shot phase noises of SWs, but have not been considered in previous repeater protocols. Here, a SW model including a homogeneous phase noise caused by SMFFs is developed, and then revealed that such phase noise induces decoherence of single‐excitation entanglement between two atomic ensembles in a repeater link. For verifying this conclusion, single‐excitation entanglement between two SWs in a cold atomic ensemble is experimentally prepared and observed entanglement decoherence induced by SMFFs. Limited by SMFFs, the evaluated lifetime of the single‐excitation entanglement over a repeater link is ≈135 ms, even if the link uses optical‐lattice atoms as nodes. Then an approach that may overcome such limitations and extend this lifetime to ≈1.7 s is presented.

Memoryless Quantum Repeaters Based on Cavity‐QED and Coherent States

AbstractA quantum repeater scheme based on cavity‐quantum electrodynamics (QED) and quantum error correction of channel loss via rotation‐symmetric bosonic codes (RSBCs) is proposed to distribute atomic entangled states over long distances without memories and at high clock rates. In this scheme, controlled rotation gates, i.e., phase shifts of the propagating light modes conditioned upon the state of an atom placed in a cavity, provide a mechanism both for the entangled‐state preparations and for the error syndrome identifications. In order to assess the performance of this repeater protocol, an explicit instance of RSBCs—multicomponent cat codes—are studied quantitatively. It is found that the total fidelity and the success probability for quantum communication over a long distance (such as 1000 km) both can almost approach unity provided a small enough elementary distance between stations (smaller than 0.1 or 0.01 km) and rather low local losses (up to 0.1%) are considered. In a quantum key distribution application, secret key rates can become correspondingly high, both per channel use, beating the repeaterless bound, and per second thanks to the relatively high clock rates of the memoryless scheme. Based upon the cavity‐QED setting, this scheme can be realized at room temperature and at optical frequencies.

Deterministic entanglement distribution on series-parallel quantum networks

The performance of distributing entanglement between two distant nodes in a large-scale quantum network (QN) of partially entangled bipartite pure states is generally benchmarked against the classical entanglement percolation (CEP) scheme. Improvements beyond CEP were only achieved by nonscalable strategies for restricted QN topologies. This paper explores and amplifies a new and more effective mapping of a QN, referred to as concurrence percolation theory (ConPT), that suggests using deterministic rather than probabilistic protocols for scalably improving on CEP across arbitrary QN topology. More precisely, we implement ConPT via a deterministic entanglement transmission (DET) scheme that is fully analogous to resistor network analysis, with the corresponding series and parallel rules represented by deterministic entanglement swapping and concentration protocols, respectively. The main contribution of this paper is to establish a powerful mathematical framework, which is applicable to arbitrary $d$-dimensional information carriers (qudits), that provides different natural optimality metrics in terms of generalized $k$-concurrences (a family of fundamental entanglement measures) for different QN topologies. In particular, we conclude that the introduced DET scheme (a) is optimal over the well-known nested repeater protocol for distilling entanglement from partially entangled qubits and (b) leads to higher success probabilities of obtaining a maximally entangled state than using CEP. The implementation of the DET scheme is experimentally feasible as tested on IBM's quantum computation platform.

All-photonic quantum repeater for multipartite entanglement generation.

Quantum network applications such as distributed quantum computing and quantum secret sharing represent a promising future network equipped with quantum resources. Entanglement generation and distribution over long distances are critical and unavoidable when utilizing quantum technology in a fully connected network. The distribution of bipartite entanglement over long distances has seen some progress, while the distribution of multipartite entanglement over long distances remains unsolved. Here we report a two-dimensional quantum repeater protocol for the generation of multipartite entanglement over long distances with an all-photonic framework to fill this gap. The entanglement generation yield remains proportional to the transmission efficiency regardless of the number of network users and shows long transmission distance under various numbers of network users. With the improved efficiency and flexibility of extending the number of users, we anticipate that our protocol can work as a significant building block for quantum networks in the future.

Distributing entanglement in first-generation discrete- and continuous-variable quantum repeaters

Quantum repeaters are used to overcome the exponential photon loss scaling that quantum states acquire as they are transmitted over long distances. While repeaters for discrete-variable encodings of quantum information have existed for some time, approaches for continuous-variable encoding quantum repeaters have only recently been proposed. In this work, we present a method of using a discrete-variable repeater protocol to distribute continuous-variable states and utilize it to compare the rates of continuous-variable entanglement distribution between first-generation continuous- and discrete-variable quantum repeaters. Such a comparison allows us to begin to benchmark the two quite different approaches.

Quantum Repeaters with Encoding on Nitrogen-Vacancy-Center Platforms

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.

Entangling single atoms over 33 km telecom fibre

Quantum networks promise to provide the infrastructure for many disruptive applications, such as efficient long-distance quantum communication and distributed quantum computing1,2. Central to these networks is the ability to distribute entanglement between distant nodes using photonic channels. Initially developed for quantum teleportation3,4 and loophole-free tests of Bell’s inequality5,6, recently, entanglement distribution has also been achieved over telecom fibres and analysed retrospectively7,8. Yet, to fully use entanglement over long-distance quantum network links it is mandatory to know it is available at the nodes before the entangled state decays. Here we demonstrate heralded entanglement between two independently trapped single rubidium atoms generated over fibre links with a length up to 33 km. For this, we generate atom–photon entanglement in two nodes located in buildings 400 m line-of-sight apart and to overcome high-attenuation losses in the fibres convert the photons to telecom wavelength using polarization-preserving quantum frequency conversion9. The long fibres guide the photons to a Bell-state measurement setup in which a successful photonic projection measurement heralds the entanglement of the atoms10. Our results show the feasibility of entanglement distribution over telecom fibre links useful, for example, for device-independent quantum key distribution11–13 and quantum repeater protocols. The presented work represents an important step towards the realization of large-scale quantum network links.

Experimental one-step deterministic polarization entanglement purification

Entanglement purification is to distill high-quality entangled states from low-quality entangled states. It is a key step in quantum repeaters, determines the efficiency and communication rates of quantum communication protocols, and is hence of central importance in long-distance communications and quantum networks. In this work, we report the first experimental demonstration of deterministic entanglement purification using polarization and spatial mode hyperentanglement. After purification, the fidelity of polarization entanglement arises from 0.268±0.002 to 0.989±0.001. Assisted with robust spatial mode entanglement, the total purification efficiency can be estimated as 109 times that of the entanglement purification protocols using two copies of entangled states when one uses the spontaneous parametric down-conversion sources. Our work may have the potential to be implemented as a part of full repeater protocols.

Multiplexed telecommunication-band quantum networking with atom arrays in optical cavities

The realization of a quantum network node of matter-based qubits compatible with telecom-band operation and large-scale quantum information processing is an outstanding challenge that has limited the potential of elementary quantum networks. We propose a platform for interfacing quantum processors comprising neutral atom arrays with telecom-band photons in a multiplexed network architecture. The use of a large atom array instead of a single atom mitigates the deleterious effects of two-way communication and improves the entanglement rate between two nodes by nearly two orders of magnitude. Further, this system simultaneously provides the ability to perform high-fidelity deterministic gates and readout within each node, opening the door to quantum repeater and purification protocols to enhance the length and fidelity of the network, respectively. Using intermediate nodes as quantum repeaters, we demonstrate the feasibility of entanglement distribution over approximately 1500 km based on realistic assumptions, providing a blueprint for a transcontinental network. Finally, we demonstrate that our platform can distribute approximately 25 Bell pairs over metropolitan distances, which could serve as the backbone of a distributed fault-tolerant quantum computer.

All-optical long-distance quantum communication with Gottesman-Kitaev-Preskill qubits

Quantum repeaters are a promising platform for realizing long-distance quantum communication and thus could form the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. Repeater protocols that encode information in single- or multi-photon states are limited by transmission losses and the cost of implementing entangling gates or Bell measurements. In this work, we consider implementing a quantum repeater protocol using Gottesman-Kitaev-Preskill (GKP) qubits. These qubits are natural elements for quantum repeater protocols, because they allow for deterministic Gaussian entangling operations and Bell measurements, which can be implemented at room temperature. The GKP encoding is also capable of correcting small displacement errors. At the cost of additional Gaussian noise, photon loss can be converted into a random displacement error channel by applying a phase-insensitive amplifier. Here we show that a similar conversion can be achieved in two-way repeater protocols by using phase-sensitive amplification applied in the post-processing of the measurement data, resulting in less overall Gaussian noise per (sufficiently short) repeater segment. We also investigate concatenating the GKP code with higher level qubit codes while leveraging analog syndrome data, post-selection, and path-selection techniques to boost the rate of communication. We compute the secure key rates and find that GKP repeaters can achieve a comparative performance relative to methods based on photonic qubits while using orders-of-magnitude fewer qubits.

Distributed Entangled State Production by Using Quantum Repeater Protocol

We consider entangled state production utilizing a full optomechanical arrangement, based on which we create entanglement between two far three-level V-type atoms using a quantum repeater protocol. At first, we consider eight identical atoms (1; 2;...; 8), while adjacent pairs (i; i + 1) with i = 1; 3; 5; 7 have been prepared in entangled states and the atoms 1, 8 are the two target atoms. The three-level atoms (1,2,3,4) and (5,6,7,8) distinctly become entangled with the system including optical and mechanical modes by performing the interaction in optomechanical cavities between atoms (2,3) and (6,7), respectively. Then, by operating appropriate measurements, instead of Bell state measurement which is a hard task in practical works, the entangled states of atoms (1,4) and (5,8) are achieved. Next, via interacting atoms (4,5) of the pairs (1,4) and (5,8) and operating proper measurement, the entangled state of target atoms (1,8) is obtained. In the continuation, entropy and success probability of the produced entangled state are then evaluated. It is observed that the time period of entropy is increased by increasing the mechanical frequency and by decreasing optomechanical coupling strength to the field modes. Also, in most cases, the maximum of success probability is increased by decreasing G and via decreasing.

Experimental demonstration of memory-enhanced scaling for entanglement connection of quantum repeater segments

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 acceleration is demonstrated in the rate for a successful entanglement connection. The experimental realization of entanglement connection of two quantum repeater segments with an efficient memory-enhanced scaling demonstrates a key advantage of the quantum repeater protocol, which makes a cornerstone towards future large-scale quantum networks.

Characterization of a surface plasmon antenna fabricated on a gate-defined lateral quantum dot

Quantum repeater composed of a quantum memory and an interface between photon qubits and memory qubits is indispensable for long-distance quantum communication. Gate-defined lateral quantum dots (QDs) can be a suitable platform for such quantum repeaters because of its aptitude for spin qubit and feasibility of quantum state transfer from photon polarization to electron spin. So far, the reported photoelectron excitation probabilities in such a QD are not high enough to implement practical repeater protocols. To improve the photoexcitation probability, we combine a surface plasmon antenna (SPA) with QDs. We fabricated a SPA designed to enhance the optical transmission to the QDs in a practical illumination setup in a refrigerator and characterized the fabricated antenna by measuring photocurrents at room temperature.