Future quantum networks will have nodes equipped with multiple quantum memories, allowing for multiplexing and entanglement distillation strategies for long-distance entanglement distribution. In this work, we focus on quasi-local policies for multiplexed quantum repeater chains. In fully-local policies, nodes use the knowledge of only their own states, whereas more efficient global policies use knowledge of the entire network state. The classical communication costs of using this knowledge have not been explored in existing literature. We show that quasi-local policies not only obtain improved performance over local policies, but also reduce classical communication costs considerably. Our policies also outperform the widely studied nested purification and doubling policy in practical parameter regimes. We identify parameter regimes where distillation is useful and address the question: “Should we distill before swapping, or vice versa?” Finally, we propose an implementation scheme for a multiplexed repeater chain, experimentally demonstrate the key element, a high-dimensional biphoton frequency comb, and evaluate its anticipated performance using our multiplexing-based policies. Fast and reliable entanglement distribution in quantum networks requires multiplexing to enhance rates and distillation to compensate the loss in fidelity. Classical communication latency associated with both swapping and distillation protocols is a significant hurdle, which the authors address by proposing a class of quasi-local entanglement distribution policies for multiplexed repeater chains.
Entanglement distillation is a fundamental operation in quantum information processing used to obtain higher-fidelity entangled pairs from a supply of less entangled quantum states using local operations aided by classical communication (LOCC). In a physically relevant setting, where states with an initial fidelity of
f0, probabilistically generated over multiple,
m, memory pairs distributed between two parties, Alice and Bob, are pairwise distilled, the optimal policy identifies the system-configuration dependent sequence of entanglement generation and distillation operations that need to be performed in order to minimize the expected time to reach some target fidelity
fT>f0. Here, we formulate and systematically analyze this task as a Markov decision problem and using a value iteration algorithm, obtain optimal deterministic policies that minimize the expected waiting time required to reach a target fidelity. Our results show that the expected waiting time under the optimal policy decreases with increasing generation probability
p and number of quantum memories
m - as expected. In contrast, it exhibits non-monotonic behavior with respect to
f0 for a fixed fidelity gap,
(Δf=fT−f0). While the optimal policy consistently outperforms baseline policies such as the greedy, nested and entanglement pumping policies, its relative advantage is regime-dependent, being determined by the system parameters (
p,f0,fT,m), and exhibits a nontrivial dependence on the fidelity gap
Δf. Our results highlight the value of formulating entanglement distillation as a Markov decision problem, enabling the systematic design of policies that achieve target fidelity thresholds for quantum information tasks in realistic resource-constrained settings.
Abstract Future quantum networks will have nodes equipped with multiple quantum memories, allowing for multiplexing and entanglement distillation. In this work, we introduce "quasi-local" policies for multiplexed quantum repeater chains. In fully-local policies, nodes make decisions based only on knowledge of their own states. In our quasi-local policies, nodes have increased knowledge of state of the repeater chain, but not necessarily global knowledge. Our policies exploit the observation that for most decisions the nodes have to make, they only need to have information about the connected region of the chain they belong to, and not the entire chain. In this way, we not only obtain improved performance over local policies, but we reduce the classical communication (CC) costs inherent to global-knowledge policies. Our policies also outperform the well-known and widely studied nested purification and doubling swapping policy in practically relevant parameter regimes. Via analytical and numerical results, we also identify the parameter regimes in which distillation makes sense and is useful. We also address the question: "Should we distill before swapping, or vice versa?'' Finally, we propose an experimental implementation of a multiplexing-based repeater chain, and experimentally demonstrate the key element, a high-dimensional biphoton frequency comb, and evaluate its anticipated performance.
Quantum repeaters are an essential building block for realizing long-distance quantum communications. However, due to the fragile nature of quantum information, these repeaters suffer from loss and operational errors. Prior works have classified repeaters into three broad categories based on their use of probabilistic or near-deterministic methods to mitigate these errors. Besides differences in classical communication times, these approaches also vary in technological complexity, with near-deterministic methods requiring more advanced hardware. Recent increases in memory availability and advances in multiplexed entanglement generation motivate a fresh comparison of one-way and two-way repeater architectures. In this work, we present a two-way repeater protocol that combines multiplexing with application-aware distillation, designed for a setting where sufficient high-quality memory resources are available—reflecting architectural assumptions expected in large-scale network deployments. We introduce a recursive formulation to track the full probability distribution of Bell pairs in multiplexed two-way repeater architectures, enabling the performance analysis of multiplexed repeater schemes which use probabilistic n-to-k distillation. Using this framework, we compare the proposed two-way protocol with one-way schemes in parameter regimes previously believed to favour the latter, and find that the two-way architecture consistently outperforms one-way protocols while requiring lower technological and resource overheads. Quantum repeaters are a fundamental building block for long-distance quantum communication, yet they face challenges from loss and operational errors. The authors introduce a two-way repeater protocol leveraging multiplexing and application-aware distillation, demonstrating superior performance and reduced resource demands compared to one-way schemes, even in scenarios previously thought to favor the latter.
Bell-state measurement (BSM) on entangled states shared between quantum repeaters is the fundamental operation used to route entanglement in quantum networks. Performing BSMs on Werner states shared between repeaters leads to exponential decay in the fidelity of the end-to-end Werner state with the number of repeaters, necessitating entanglement distillation. In this work, we use quantum error correcting codes for deterministic entanglement distillation to route Werner states on a chain of repeaters. To maximize the end-to-end distillable entanglement, we utilize global link-state knowledge to determine the optimal policy for scheduling distillation and BSMs at the repeaters. We observe that low-rate codes produce high-fidelity end-to-end states owing to their excellent error-correcting capability, whereas high-rate codes yield a larger number of end-to-end states but of lower fidelity. The number of quantum memories used at repeaters increases with the code rate as well as the classical computation time of the decoder.
Quantum communication enables the implementation of tasks that are unachievable with classical resources. However, losses on the communication channel preclude the direct long-distance transmission of quantum information in many relevant scenarios. In principle, quantum repeaters allow one to overcome losses. However, realistic hardware parameters make long-distance quantum communication a challenge in practice. For instance, in many protocols an entangled pair is generated that needs to wait in quantum memory until the generation of an additional pair. During this waiting time the first pair decoheres, impacting the quality of the final entanglement produced. At the cost of a lower rate, this effect can be mitigated by imposing a cutoff condition. For instance, a maximum storage time for entanglement after which it is discarded. In this article, we optimize the cutoffs for quantum repeater chains. First, we develop an algorithm for computing the probability distribution of the waiting time and fidelity of entanglement produced by repeater chain protocols which include a cutoff. Then, we use the algorithm to optimize cutoffs in order to maximize the secret-key rate between the end nodes of the repeater chain. In this article, we find that the use of the optimal cutoff extends the parameter regime for which secret key can be generated and, moreover, significantly increases the secret-key rate for a large range of parameters.