Macroscopic entanglement distribution with atomic ensembles

Annals of Physics. 2026. Vol. 494. Article 170618.

Li S., Hu J., Lazarev I., Raghoonanan J., Ivannikov V., Pyrkov A., Byrnes T.

The distribution of entanglement is a crucial task for quantum communication towards realizing a globe-spanning quantum internet. Recently, a protocol for deterministic long-distance distribution of macroscopic entanglement over a network of ensembles of qubits was introduced (Pyrkov et al., 2025). It was shown that this protocol allows for the propagation of macroscopic amounts of entanglement with a protocol complexity that is independent on the ensemble size. However, questions remained on whether the scheme is viable, particularly for a large particle number, which is the case for realistic atomic ensembles. Here, we develop improved numerical techniques that allow the ideal, decoherence-free protocol to be calculated for ensemble sizes up to 𝑁∼1⁢06 with negligible loss of numerical accuracy. We also include collective 𝑆𝑧 dephasing for finite systems up to 𝑁=30, finding that moderate dephasing leaves the branch entanglement largely intact at the magic times, whereas stronger noise suppresses the entanglement. Our results demonstrate large-𝑁 scalability of the ideal protocol and provide finite-size benchmarks for its robustness under collective dephasing.

Keywords: quantum communication