Towards a General Framework for Practical Quantum Network Protocols

Quantum network is a promising platform for numerous quantum applications, including distributed quantum computing, secure communication, and improved sensing. Implementing entanglement distribution between remote quantum nodes plays a vital role in realizing the quantum network's capabilities, and it requires effective remote entanglement distribution protocols. To meet this requirement, we propose two strategies, namely connection-oriented and connectionless, to achieve end-to-end entanglement distribution inspired by the designs of classical communication. For the connection-oriented strategy, an exclusive quantum connection is pre-established between the source and destination nodes. For the connectionless strategy, entanglement swapping is performed hop-by-hop tentatively. In this way, the best-effort service is provided for the source node to establish long-distance entanglement with the destination node. Analogous to classical communication, the proposed strategies have their advantages and disadvantages. Our simulation results show that the connectionless strategy is more efficient and robust than the connection-oriented strategy in terms of throughput. However, the connection-oriented strategy provides reliable end-to-end entanglement distribution but at the expense of higher overhead. Moreover, the application scenarios of these two strategies are discussed. This work paves the road for designing end-to-end entanglement distribution protocols in quantum networks.

A key technical requirement of any future quantum network is the ability to distribute quantum-entangled resources between two spatially separated points at a high rate and high fidelity. Entanglement distribution protocols based on satellite platforms, which transmit and receive quantum resources directly via free-space optical propagation, are therefore excellent candidates for quantum networking, since the geometry and loss characteristics of satellite networks feasibly allow for up to continental-scale ($\sim10^3$ km) over-the-horizon communication without the infrastructure, cost, or losses associated with equivalent fibre-optic networks. In this work, we explore two network topologies commonly associated with quantum networks - entanglement distribution between two satellites in low-Earth orbit mediated by a third satellite and entanglement distribution between two ground stations mediated by a satellite in low-Earth orbit, and two entanglement distribution schemes - one where the central satellite is used as a relay, and the other where the central satellite is used to generate and distribute the entangled resource directly. We compute a bound on the rate of distribution of distillable entanglement achieved by each protocol in each network topology as a function of the network channels for both single-rail discrete- (DV) and continuous-variable (CV) resources and use or non-use of probabilistic noiseless linear quantum amplification (NLA). In the case of atmospheric channels we take into account the turbulent and optical properties of the free-space propagation. We determine that for the triple-satellite network configuration, the optimal strategy is to perform a distributed NLA scheme in either CV or DV, and for the ground-satellite-ground network the optimal strategy is to distribute a DV resource via the central satellite.

A deterministic entanglement distribution protocol (EDP) is proposed in principle for transmitting a maximally entangled W state over collective-noise channels. Using this EDP, a W state can be reconstructed directly from a three-photon entangled state in the frequency degree of freedom prepared among three remote participants due to the fact that it suffers little from the channel noise. In essence, it is a entanglement transformation between different degrees of freedom in three-photon entangled system. This EDP adopts the cross-Kerr nonlinearity media to complete the task of the single-photon detections, which can increase the efficiency of entanglement distribution since it does not require the sophisticated single-photon detectors for the usual measurements and the retained photons can be still held solely by three respective participants after entanglement distillation.

Time-bin entangled photons allow robust entanglement distribution over quantum networks. Integrated photonic circuits positioned at the nodes of a quantum network can perform the important functions of generating highly entangled photons and precisely manipulating their quantum state. In this Letter, we demonstrate time-bin entangled photon generation, noise suppression, wavelength division, and entanglement analysis on a single photonic chip utilizing low-loss double-stripe silicon nitride waveguide structures. Quantum state tomography results show 91±0.7% fidelity compared with the ideal state, indicating that highly entangled photons are generated and analyzed. This work represents a crucial step toward practical quantum networks.

Large-scale quantum networks with thousands of nodes require scalable network protocols and physical hardware to realize. In this paper, we introduce packet switching as a paradigm for quantum data transmission in both future and near-term quantum networks. We propose a classical-quantum data frame structure and explore methods of frame generation and processing. Further, we present conceptual designs for a quantum reconfigurable optical add-drop multiplexer to realize the proposed transmission scheme. Packet switching allows for a universal design for a next-generation Internet where classical and quantum data share the same network protocols and infrastructure. In this quantum networking paradigm, entanglement distribution, as with quantum key distribution, is an application built on top of the quantum network rather than as a network designed especially for those purposes. For analysis of the network model, we simulate the feasibility of quantum packet switching for some preliminary models of quantum key and entanglement distribution. Finally, we discuss how our model can be integrated with other network models toward a realization of the quantum Internet.

We propose an efficient nonlocal entanglement distribution protocol (EDP) to purify the two-photon polarization-entangled state, resorting to the projection measurement on the additional photons. With the help of the cross-Kerr nonlinearity, two remote parties can share two-photon maximally entangled polarization state from the arbitrary two-photon states with a certain success probability by iterating the entanglement purification process 6 times. Compared with conventional EDPs, the present one can obtain maximally entangled polarization state over an collective-noise channel with deterministic success probability. That is, the EDP is an optimal one.

Quantum secure direct communication (QSDC) offers a practical way to realize a quantum network which can transmit information securely and reliably. Practical quantum networks are hindered by the unavailability of quantum relays. To overcome this limitation, a proposal has been made to transmit the messages encrypted with classical cryptography, such as post-quantum algorithms, between intermediate nodes of the network, where encrypted messages in quantum states are read out in classical bits, and sent to the next node using QSDC. In this paper, we report a real-time demonstration of a computationally secure relay for a quantum secure direct communication network. We have chosen CRYSTALS-KYBER which has been standardized by the National Institute of Standards and Technology to encrypt the messages for transmission of the QSDC system. The quantum bit error rate of the relay system is typically below the security threshold. Our relay can support a QSDC communication rate of 2.5 kb/s within a 4 ms time delay. The experimental demonstration shows the feasibility of constructing a large-scale quantum network in the near future.

Quantum information technology has been developing rapidly in last two decades. Very recently, quite a few optical quantum key distribution networks have been reported, enabling preliminary practical applications in secure information transfer. Meanwhile, a number of significant progresses based on quantum network have also been made in the research of linear optical quantum computing, simulation and metrology. However, on the way towards large-scale optical quantum network serious problems occur. On the one hand, the distance of fiber-based quantum communication is limited, due to intrinsic fiber loss and decreasing of entanglement quality caused by the noisy environment. On the other hand, the probabilistic feature of single and entangled photon sources would also cause an exponentially increasing overhead for large-scale quantum network. To solve the above problems, quantum repeaters and/or transmission of optical quantum bits over free space channel can be efficiently exploited for future wide-area realization of quantum communication. In addition, memory built-in quantum repeaters would also enable scalable linear optical quantum computing, simulation and high precision measurement. In this talk I will present some recent experiments from our group, including eight-photon entanglement, topological quantum error-correction, quantum repeater and efficient and long-lived quantum memory, and entanglement distribution and quantum teleportation over 100km-scale free-space quantum channels. These experiments show the promising future possibility towards scalable quantum network with photons and atoms.

With their ability to process and transfer quantum information, large-scale entanglement-based quantum networks could be at the heart of a new age of quantum information, enabling fundamentally new applications such as distributed quantum computation, quantum communication, and quantum enhanced sensing. Due to their long spin coherence, controllable local qubit registers and optically active spins, color centers in diamond are prime candidates for nodes of such a network, and have enabled some of the most advanced quantum network demonstrations to date. These demonstrations include the distribution of a 3-node GHZ state across a quantum network, entanglement swapping, entanglement distillation, and memory-enhanced quantum communication. To move beyond current proof-of-principle networks, a further increase of entanglement generation rates is crucial. This thesis presents theoretical and experimental work on enhancing the spin-photon interface of color centers in diamond to achieve this goal, making use of the Purcell effect. The discussed work follows two main directions: embedding of color centers in open, tuneable Fabry-Perot micro-cavities, and in all-diamond photonic crystal cavities. First, we describe theoretical and experimental progress towards cavity-enhanced quantum networks based on nitrogen-vacancy (NV) centers in diamond. Due to their first order sensitivity to electric fields, we choose to embed NV centers in microns-thin diamond membranes that can be integrated into open fiber-based micro-cavities. We develop analytical methods to optimize the design of such open cavity systems for maximum Purcell enhancement of embedded color centers. We demonstrate a method to fabricate optically coherent NV centers in microns-thin diamond membranes, and use such structures to demonstrate the resonant excitation and detection of coherent, Purcell enhanced NV emission. A theoretical model in excellent agreement with our results suggests our system can improve entanglement rates between distant NV centers by two orders of magnitude with near-term improvements to the setup. Second, we describe progress towards an efficient spin-photon interface of group-IV color centers in diamond by coupling them to photonic nanostructures, allowing for large-scale integration. Due to their first-order insensitivity to electric fields, group-IV color centers can be brought in close proximity to surfaces (~ 100 nm), allowing for sub-wavelength mode volumes and thus very high Purcell factors. We numerically optimize photonic crystal cavity designs to maximize the Purcell enhancement of embedded emitters, test the robustness of our designs to real-world fabrication imperfections, and devise a method to efficiently interface nanophotonic structures. We then proceed to fabricate all-diamond photonic crystal cavities, making use of a dry etching technique that is selective to different crystallographic directions, and characterize the resulting optical quality factors. Finally, we marry the developed fabrication methods to fabricate microns-sized diamond platelets that can be transferred from a holding frame in a controlled fashion. This capability could be crucial for the realization of hybrid photonic circuits that we expect to be at the heart of future large-scale quantum networks.

Quantum mechanics allows an information carrier to traverse through multiple trajectories of communication channels simultaneously, this leads us to quantum trajectories where alternative causal orders of communication channels being traversed are in a superposition, so that the relative orders of communication channels become indefinite. It has been shown that entanglement distribution process over quantum trajectory with an EPR pair being prepared by a sender enables quantum teleportation process to be heralded as a noiseless communication process with probability, the heralded result of which is unachievable in classical trajectory with a definite causal order of communication channels. In this work, we investigate the potential advantage of quantum trajectory on the generation of link-level entanglement, the basic element of quantum networks. To this aim, the performance of entanglement distribution process over multiple quantum trajectories where an EPR pair is prepared by a communication provider is analyzed. Besides, the application of entanglement purification protocol on quantum trajectory is first analyzed to reduce the effect of noise on link-level entanglement. The analysis shows that the link-level entanglement generated over quantum trajectory is more robust to long-distance quantum communication, with respect to classical trajectory, which paves the way for designing effective quantum networks.

The past decade has seen tremendous progress in experimentally realizing the building blocks of quantum repeaters. Repeater architectures with multiplexed quantum memories have been proposed to increase entanglement distribution rates, but an open challenge is to maintain entanglement fidelity over long-distance links. Here, we address this with a quantum router architecture comprising many quantum memories connected in a photonic switchboard to broker entanglement flows across quantum networks. We compute the rate and fidelity of entanglement distribution under this architecture using an event-based simulator, finding that the router improves the entanglement fidelity as multiplexing depth increases without a significant drop in the entanglement distribution rate. Specifically, the router permits channel-loss-invariant fidelity, i.e. the same fidelity achievable with lossless links. Furthermore, this scheme automatically prioritizes entanglement flows across the full network without requiring global network information. The proposed architecture uses present-day photonic technology, opening a path to near-term deployable multi-node quantum networks.

Entangled states shared among distant nodes are frequently used in quantum network applications. When quantum resources are abundant, entangled states can be continuously distributed across the network, allowing nodes to consume them whenever necessary. This continuous distribution of entanglement enables quantum network applications to operate continuously while being regularly supplied with entangled states. Here, we focus on the steady-state performance analysis of protocols for continuous distribution of entanglement. We propose the virtual neighborhood size and the virtual node degree as performance metrics. We utilize the concept of Pareto optimality to formulate a multiobjective optimization problem to maximize the performance. As an example, we solve the problem for a quantum network with a tree topology. One of the main conclusions from our analysis is that the entanglement consumption rate has a greater impact on the protocol performance than the fidelity requirements. The metrics that we establish in this paper can be utilized to assess the feasibility of entanglement distribution protocols for large-scale quantum networks.

Distributing entanglement efficiently across quantum networks remains a major challenge, primarily due to the intricate timing and coordination required for entanglement generation and swapping. Orchestrating these operations with precision is key to achieving efficient and reliable entanglement distribution while hardware performance is improved.

Flexible grid wavelength division multiplexing is a powerful tool in lightwave communications to maximize spectral efficiency. In the emerging field of quantum networking, the need for effective resource provisioning is particularly acute, given the generally lower power levels, higher sensitivity to loss, and inapplicability of optical detection and retransmission. In this letter, we leverage flex grid technology to demonstrate reconfigurable distribution of quantum entanglement in a four-user tabletop network. By adaptively partitioning bandwidth with a single wavelength-selective switch, we successfully equalize two-party coincidence rates that initially differ by over two orders of magnitude. Our scalable approach introduces loss that is fixed with the number of users, offering a practical path for the establishment and management of quality-of-service guarantees in large quantum networks.

The generation, distribution and control of entanglement across quantum networks is one of the main goals of quantum information science. In previous studies, hyperfine ground states of single atoms or atomic ensembles have been entangled with spontaneously emitted light. The probabilistic character of the spontaneous emission process leads to long entanglement generation times, limiting realized network implementations to just two nodes. The success probability for atom-photon entanglement protocols can be increased by confining a single atom in a high-finesse optical cavity. Alternatively, quantum networks with superior scaling properties could be achieved using entanglement between light fields and atoms in quantum superpositions of the ground and highly excited (Rydberg) electronic states. Here we report the generation of such entanglement. The dephasing of the optical atomic coherence is inhibited by state-insensitive confinement of both the ground and Rydberg states of an ultracold atomic gas in an optical lattice. Our results pave the way for functional, many-node quantum networks capable of deterministic quantum logic operations between long-lived atomic memories.