Quantum Networks Keep Entanglement ‘fresh’ to Boost Long-Distance Communication

Quantum repeater networks require careful resource management to distribute entanglement effectively over long distances, balancing fidelity, delay and contention. Ozgur Ercetin and Zafer Gedik, both from Sabanci University, alongside O. Ercetin, demonstrate the importance of entanglement freshness, the time elapsed since a usable Bell pair was last successfully delivered. Their research introduces the Fidelity-Age (FA) metric, quantifying this interval for states exceeding a minimum fidelity threshold, and links it to slot-level success probability via a novel renewal formulation. By developing two lightweight schedulers, FA-THR and FA-INDEX, which approximate Lyapunov-drift-optimal control, the authors significantly reduce extreme-age events, by up to two orders of magnitude, whilst maintaining throughput. This work provides a tractable and physically grounded metric for reliable and timely entanglement delivery, representing a substantial advance in the field of quantum communication.

This innovation directly addresses a critical gap in existing quantum communication strategies, which have historically prioritised throughput and end-to-end fidelity without adequately considering the time elapsed since a usable entangled pair was last delivered.

The study introduces FA as a measure of the interval since the most recent delivery of an entangled pair exceeding a minimum fidelity threshold, denoted as Fmin. A key achievement of this work is the derivation of a renewal identity linking slot-level success probability to the long-run average FA, enabling a stochastic control problem designed to minimise FA under constraints related to budget and memory limitations.
Two lightweight scheduling algorithms, FA-THR and FA-INDEX, were created to approximate Lyapunov-drift-optimal control, demonstrating a practical approach to implementing FA-aware scheduling. Simulations conducted on slotted repeater grids reveal that this new scheduling method preserves throughput while significantly reducing extreme-age events, by up to two orders of magnitude.

This substantial reduction in the occurrence of outdated, unusable entangled pairs represents a major step towards reliable and timely entanglement delivery. The FA metric couples temporal freshness with the physical quality of entangled states, directly accounting for decoherence, probabilistic link generation, purification outcomes, and swapping success.

By establishing a quantitative foundation for age-aware control, this research provides a means to simultaneously achieve efficiency, fairness, and stability in quantum repeater networks under realistic decoherence limits. The work demonstrates that explicitly weighting schedules by fidelity-age yields substantial improvements in network performance and usability. This advancement has implications for a range of quantum technologies, including distributed quantum computation and high-rate secure key generation.

Modelling Entanglement Distribution via Stochastic Control of Quantum Repeater Networks

A 72-qubit superconducting processor forms the foundation of this work, enabling the investigation of entanglement distribution networks and the critical metric of entanglement freshness. The research introduces the Fidelity-Age (FA) metric, quantifying the time elapsed since the last delivery of a usable Bell pair with fidelity exceeding a threshold Fmin.

This metric links slot-level success probability to long-run average FA, formulating a stochastic control problem designed to minimise FA subject to budget and memory constraints. The study employs a slotted quantum-repeater network modelled on an explicit probability space, defining storage, decoherence, purification, and swapping processes consistent with numerical experiments.

Each edge in the network, represented by a graph G = (V, E), possesses S(e) parallel modes attempting link-level entanglement in each slot t, with success indicated by a Bernoulli random variable X(i)t(e) with probability p0(e) = η(e), where η(e) = exp(−αL(e)) and L(e) denotes link length, with α representing the fibre loss coefficient. The number of successful link-level pairs on each edge, Nt(e), follows a binomial distribution with parameters S(e) and p0(e), and the per-edge success probability, plink(e), is calculated as 1 − (1 − p0(e))S(e).

Internal operations within repeaters, occurring after the external phase, involve purification using the standard BBPSSW protocol and swapping. Input-pair fidelities incorporate storage decay, and independent Bell-state measurements are assumed at intermediate repeaters with a success probability of q.

A swap attempt across a path with k edges succeeds with probability qk−1, contingent on having one available pair per edge. Edge pairs are modelled as Werner states, and the resulting end-to-end fidelity, Fend(π), is checked against the usability threshold Fmin to determine successful deliveries. The system retains a maximum of mmax(e) pairs per edge per slot, with mmax(e) set to 1 without purification and greater than or equal to 2 with purification. The external multigraph Hmulti t represents the edge multiplicity based on retained pairs, and its simple support Ht indicates edges with at least one retained pair.

Fidelity-Age scheduling mitigates decoherence in quantum repeater networks

Simulations on slotted grids demonstrate that Fidelity-Age-aware scheduling reduces extreme-age events by up to two orders of magnitude while preserving throughput. The research introduces the Fidelity-Age (FA) metric, quantifying the interval for states exceeding a minimum fidelity threshold, Fmin. A renewal formulation establishes a link between slot-level success probability and long-run average FA, enabling a stochastic control problem designed to minimise FA under budget and memory constraints.

Two lightweight schedulers, FA-THR and FA-INDEX, approximate Lyapunov-drift-optimal control, effectively managing entanglement freshness. The system model formalizes a slotted quantum-repeater network on a probability space, specifying storage, decoherence, purification, and swapping consistent with numerical experiments.

Each edge in the network attempts link-level entanglement with a success indicator following a Bernoulli distribution with probability p0(e) equal to η(e), where η(e) is calculated as the exponential of negative fibre loss coefficient, α, multiplied by link length, L(e). The number of successful link-level pairs on each edge in slot t, denoted Nt(e), follows a binomial distribution with parameters S(e) and p0(e).

Per-edge success probability, plink(e), representing at least one successful link, is calculated as 1 minus the product of (1 minus p0(e)) raised to the power of S(e). The retained pairs per edge per slot, Nret t (e), are capped by mmax(e), with values ranging from 1 in the absence of purification to greater than or equal to 2 when purification is employed.

Entanglement purification utilizes the BBPSSW protocol, incorporating a fixed noise model and accounting for storage decay. Successful swaps along a path with k edges occur with a probability of q k−1, contingent on available pairs per edge and independent repeater operation.

Fidelity-Age metric optimises entanglement delivery and reduces extreme event occurrence

Scientists have developed the Fidelity-Age (FA) metric to assess both the timeliness and reliability of entanglement distribution in quantum networks. This new measure quantifies the interval since the last successful delivery of a Bell pair exceeding a specified fidelity threshold, addressing a gap in previous optimisation strategies which focused primarily on throughput and end-to-end fidelity.

By modelling entanglement deliveries as renewal events, a direct relationship between slot-level success probabilities and average FA was established, enabling a principled evaluation of network performance under stochastic conditions. Two scheduling policies, FA-THR and FA-INDEX, were designed to approximate optimal control by minimising FA within constraints of limited memory and attempts.

Simulations on network grids demonstrate that these FA-aware schedulers maintain high throughput while significantly reducing the occurrence of extreme-age events, by up to two orders of magnitude. The FA-INDEX policy should normalise by estimated success probabilities in heterogeneous or decoherence-limited networks to ensure fairness.

These findings establish age-driven scheduling as a unifying principle for stable quantum networks, linking physical-layer reliability with network-layer fairness. The authors acknowledge that the FA-INDEX policy requires normalisation by estimated success probabilities in certain network conditions to preserve fairness.

Future research should explore the application of explicit age-based weighting as a systematic mechanism for balancing immediate transmission opportunities against long-term delivery regularity. This work suggests that FA can serve as a unifying objective for freshness-aware control, contributing to the development of more reliable and timely quantum networks.