Locally Heralded Distribution Protocol

• Locally Heralded Distribution (LHD) is a repeater-chain protocol that uses local nearest-neighbor heralding to optimize entanglement distribution while avoiding unnecessary Bell-state measurements.
• It employs parallel elementary-pair generation with a fixed one-slot heralding exchange, reducing waiting time compared to globally coordinated schemes.
• Simulations show LHD improves link probability under imperfect memory conditions, though its longer protocol duration can lead to lower final fidelity compared to blind swapping.

Locally Heralded Distribution (LHD) is an entanglement-distribution protocol for repeater chains introduced as a modification of a memory- and fidelity-aware version of Globally Heralded Distribution (GHD), itself built from the “Unheralded Swapping” idea discussed in \cite{Abane25}. Its defining idea is to preserve the benefit of informed swapping—avoiding unnecessary Bell-state measurements (BSMs) and wasted entangled pairs—while replacing route-wide coordination by nearest-neighbor heralding information, thereby shortening execution time and improving performance when memories are imperfect (Mesny et al., 29 May 2026). In this usage, “locally heralded” refers specifically to heralding information generated and exchanged only between nearest neighbors, concerning local distribution outcomes—“which photons have been received and which of the stored photons have been lost”—rather than to a central or end-to-end controller (Mesny et al., 29 May 2026).

1. Definition within repeater-chain protocols

LHD is formulated for the standard long-distance entanglement-distribution problem in a linear repeater route $r$ with $l_r$ nodes and $l_r-1$ elementary links. The destination is labeled $l_r$, so the route contains $n_r=l_r-1$ transmitting nodes. Link $i$ has physical length $L_i$ and attenuation parameter $\alpha_i$, while node $i$ has a quantum memory with mean lifetime $\tau_i$. Time is slotted with slot duration $l_r$0. On each elementary link, an entangled pair is generated at node $l_r$1, with one photon kept locally in memory and the other sent to node $l_r$2. Intermediate repeaters eventually receive one half-pair from the left and one from the right and can perform a BSM to swap them; after all successful swaps and LOCC notification, the source and destination share an end-to-end pair (Mesny et al., 29 May 2026).

The protocol is best understood by contrast with the two baseline schemes used in the same study. In Blind Swapping (BS), each repeater swaps immediately at the end of a slot without knowing whether adjacent segments both succeeded. In GHD, nodes use route-wide information: a global minimum number of successfully distributed pairs is computed across the path, and all swapping nodes are instructed accordingly. LHD sits between these extremes. It is not blind, because each repeater swaps only the number of pairs actually available on both sides locally; but it is not globally coordinated either, because it uses only nearest-neighbor information and therefore incurs a fixed one-slot coordination cost rather than a route-length-dependent one (Mesny et al., 29 May 2026).

This nearest-neighbor structure is the precise sense in which the protocol is “locally heralded.” The heralding data are generated at link endpoints from local delivery and storage outcomes and consumed by adjacent swapping nodes. A plausible implication is that LHD should be classified as a distributed local-feedforward protocol rather than as a midpoint-heralded or centrally scheduled elementary-link protocol.

2. Operational structure and timing model

Mechanically, LHD proceeds in width-$l_r$3 batches of elementary-generation attempts. For each $l_r$4, the number of successful elementary distributions on link $l_r$5 is modeled as

$l_r$6

where $l_r$7 is the success probability that a single elementary pair survives fiber transmission and memory waiting. After these parallel attempts, each node sends its local distribution-outcome information to its nearest neighbors; this one-hop classical exchange takes one time slot. Each repeater then computes the local minimum number of usable adjacent pairs from the left and right sides and performs only that many local BSMs. Finally, BSM outcomes are propagated to the endpoints over $l_r$8, traversed toward both ends in parallel (Mesny et al., 29 May 2026).

The crucial timing claim is that LHD shortens the pre-swap waiting time. In GHD, all nodes must effectively wait for route-wide collection and redistribution of distribution outcomes, so coordination time scales with route length. In LHD, the coordination phase lasts one slot regardless of $l_r$9. Since memory loss and memory/fiber decoherence are modeled exponentially in waiting time, the reduction from a route-length-dependent delay to a fixed one-slot delay is the protocol’s central systems-level advantage (Mesny et al., 29 May 2026).

The single-attempt elementary-link success probability is written as

$l_r-1$0

and simplified as

$l_r-1$1

with

$l_r-1$2

In plain terms, $l_r-1$3 combines fiber attenuation, survival of the received half in the destination memory until the end of the slot, and survival of the retained half in the source memory for the whole slot (Mesny et al., 29 May 2026).

3. Noise, success probability, and fidelity model

The physical model couples attenuation, memory loss, decoherence, and stochastic swapping. Fiber transmission over distance $l_r-1$4 with attenuation parameter $l_r-1$5 is modeled by

$l_r-1$6

with the paper noting that typical telecom fiber has $l_r-1$7. Elementary entangled states are modeled as Werner states,

$l_r-1$8

and decohere toward $l_r-1$9 according to

$l_r$0

Memory loss is exponential,

$l_r$1

and swapping succeeds with probability

$l_r$2

while reducing fidelity via

$l_r$3

The write-in and read-out operations are assumed deterministic for simplification (Mesny et al., 29 May 2026).

For BS, the end-to-end single-attempt success probability is

$l_r$4

with

$l_r$5

For GHD and LHD, the paper uses the same mixture structure based on the bottleneck number of available elementary pairs. If $l_r$6 denotes the minimum number of successful elementary distributions across the route, then

$l_r$7

with

$l_r$8

Conditionally,

$l_r$9

where

$n_r=l_r-1$0

The corresponding GHD parameter differs by the route-length-dependent waiting penalty before swapping (Mesny et al., 29 May 2026).

The same timing distinction appears in the fidelity model. For LHD, the initial pair fidelity before swapping is

$n_r=l_r-1$1

whereas GHD replaces $n_r=l_r-1$2 by $n_r=l_r-1$3. This means that local heralding reduces pre-swap storage to about two slots minus propagation time—one slot for generation/distribution and one slot for nearest-neighbor exchange—so fidelity is preserved much better than in GHD (Mesny et al., 29 May 2026).

4. Comparative performance and regime of advantage

The benchmarking methodology is simulation-based, implemented in Python, with BS as the baseline. The reported simulation parameters are width $n_r=l_r-1$4 generations, distance between nodes $n_r=l_r-1$5, attenuation parameter $n_r=l_r-1$6, fiber propagation speed $n_r=l_r-1$7, and memory lifetime $n_r=l_r-1$8 for all nodes. Under these assumptions, simulation and theory are said to agree well (Mesny et al., 29 May 2026).

The principal result is probabilistic rather than absolute-rate based: LHD clearly outperforms both GHD and BS in link probability, and the gap widens with route length. The paper reports

$n_r=l_r-1$9

while

$i$0

This is the study’s strongest route-length scalability statement. The stated reason is entirely the shorter memory-storage duration induced by local coordination (Mesny et al., 29 May 2026).

The comparison is more nuanced for fidelity. For $i$1, GHD shows a “dramatic decrease” in fidelity with increasing route length, whereas LHD offers a “great improvement” over GHD. However, BS can still be بہتر on fidelity alone because it swaps sooner; the paper explicitly states that “The longer protocol duration of LHD compared with Blind Swapping makes the final link fidelity lower.” The claimed advantage of LHD is therefore a probability/resource-efficiency advantage under imperfect memories, not uniform dominance on every metric (Mesny et al., 29 May 2026).

The authors’ own scope conditions are narrow. The protocol is analyzed only on a single route; deterministic memory write/read is assumed; independent gate-error channels, detector inefficiency, dark counts, and source multipair noise are omitted; and the local-minimum decision rule is described architecturally rather than with a separate combinatorial law distinct from the global-minimum variable $i$2. This suggests that LHD, as introduced, is a practical near-term improvement in principle rather than a fully implementation-ready network stack (Mesny et al., 29 May 2026).

5. Relation to heralded-link experiments and adjacent architectures

Several recent and earlier quantum-network papers are closely related to LHD, but the relationship is usually architectural rather than terminological. The most direct conceptual relatives are heralded-distribution schemes in which remote qubits are preserved while an auxiliary detection pattern certifies success. “Towards heralded distribution of polarization entanglement” constructs a single quantum repeater link from four single-photon inputs, with a central heralding station whose click pattern ideally projects remote modes $i$3 and $i$4 onto $i$5. The paper distinguishes sharply between the genuinely heralded state without postselection and the fourfold postselected state; its reported postselected fidelity is $i$6, while the non-postselected heralded state is much lower in the present implementation (Marcellino et al., 2023). This is close to LHD in intent, but the herald is central rather than end-node local.

“Heralded distribution of single-photon path entanglement” realizes a repeater-like architecture in which two idler photons interfere at a central station, and a single detector click heralds remote single-photon path entanglement over 2 km of optical fiber at a rate of $i$7 (Caspar et al., 2020). The heralding event is again central-station interference, not nearest-neighbor local outcome exchange. Likewise, “Heralded entanglement distribution between two absorptive quantum memories” demonstrates an elementary link with two absorptive memories and a midpoint BSM; the herald certifies successful distribution of entanglement between the memories, but the signal is generated at the central station, so the correct characterization is midpoint Bell-state-measurement heralding rather than strict local heralding (Liu et al., 2021).

Other papers illuminate narrower primitives. “Heralded photon amplification for quantum communication” demonstrates a receiver-side heralding signal generated locally at the amplifier node by interfering an incoming lossy mode with a local auxiliary photon; the protocol conditionally increases the single-photon component relative to vacuum, but it is not an entanglement-distribution protocol on its own (Osorio et al., 2012). “Heralded amplification of nonlocality via entanglement swapping for long-distance device-independent quantum key distribution” uses a central entanglement-swapping relay; this is event-ready heralded distribution, but not purely end-node-local heralding (Tsujimoto et al., 2019). Finally, “Heralded optical entanglement distribution via lossy quantum channels: A comparative study” introduces a decentralized-heralding SD scheme in which heralding detectors are evenly distributed among all participants rather than concentrated at a hub; this is the closest match to LHD at the detector-placement level, although the success event is still a global coincidence pattern across all local modules (Zo et al., 2024).

Taken together, these papers delineate a spectrum: receiver-local heralding primitives, midpoint-heralded elementary links, centralized event-ready architectures, and decentralized detector layouts. LHD, in the strict sense introduced in (Mesny et al., 29 May 2026), occupies the niche in which nearest-neighbor heralding data drive local swap decisions in a repeater chain.

6. Terminological boundaries, misconceptions, and acronym ambiguity

A common misconception is to treat any heralded entanglement-distribution protocol as an instance of LHD. The literature summarized above shows that this is too broad. Midpoint BSM schemes can be heralded without being locally heralded in the strict sense; central event-ready ESR protocols can distribute useful nonlocal resources without replacing nearest-neighbor local coordination; and receiver-side heralded amplification can supply a local flag without itself establishing remote entanglement. LHD, as defined in (Mesny et al., 29 May 2026), is specifically a repeater-chain protocol in which only nearest-neighbor heralding information is exchanged before swapping.

Another boundary concerns decentralization. Distributed detector placement does not by itself imply fully local autonomous heralding. In the SD architecture of (Zo et al., 2024), detector modules are decentralized, but the heralding condition is still a network-wide pattern that must be classically combined. This suggests a distinction between decentralized heralding and nearest-neighbor locally heralded swap control.

Finally, the acronym “LHD” is heavily overloaded on arXiv. In unrelated plasma-physics literature it usually denotes the Large Helical Device rather than Locally Heralded Distribution, as in work on core density collapse, sawtooth-like activity, or stellarator gyrokinetics (Civit et al., 2024). In quantum-network contexts, therefore, the expanded form is often necessary to avoid ambiguity.

LHD is thus best understood as a specific protocol family within repeater-chain control: parallel elementary-link generation, one-slot nearest-neighbor herald exchange, locally justified swapping, and endpoint LOCC notification. Its importance arises from the fact that imperfect memories make waiting costly; its distinctiveness lies in reducing coordination delay without reverting to blind swapping (Mesny et al., 29 May 2026).