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Macroscopic entanglement distribution with atomic ensembles

Shuang Li, Jin Hu, Ilia D. Lazarev, Jonathan Raghoonanan, Valentin Ivannikov, Alexey N. Pyrkov, Tim Byrnes

Abstract

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 [Adv. Quantum Technol. 2025, 8, 2400524]. 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 calculation of realistic ensemble sizes up to 10^6 with a negligible loss of accuracy. We find that moderate dephasing leaves the entanglement largely intact at the magic times, whereas stronger noise monotonically suppresses the entanglement. Our results demonstrate that the protocol retains its functionality towards the macroscopic regime and provides quantitative benchmarks for its robustness under a realistic level of decoherence.

Macroscopic entanglement distribution with atomic ensembles

Abstract

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 [Adv. Quantum Technol. 2025, 8, 2400524]. 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 calculation of realistic ensemble sizes up to 10^6 with a negligible loss of accuracy. We find that moderate dephasing leaves the entanglement largely intact at the magic times, whereas stronger noise monotonically suppresses the entanglement. Our results demonstrate that the protocol retains its functionality towards the macroscopic regime and provides quantitative benchmarks for its robustness under a realistic level of decoherence.
Paper Structure (15 sections, 33 equations, 4 figures)

This paper contains 15 sections, 33 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Quantum repeater for distributing macroscopic entanglement
  3. Physical system
  4. The protocol
  5. Initial state
  6. Entanglement generation
  7. Measurement
  8. Quantifying entanglement
  9. Decoherence
  10. Numerical methods
  11. Method I: Exact simulation
  12. Method II: Fock space truncated window approximation
  13. Decoherence-free case
  14. Including Decoherence
  15. Summary and Conclusions

Figures (4)

  • Figure 1: The end--to--end entanglement without normalization (\ref{['entropy']}) for the chain $M=3$ and the ensemble sizes as marked. The sizes of the truncated window in Fock space for different N are also marked.
  • Figure 2: Precision of the entanglement calculation with the Fock space truncated window approximation method (a) comparison of entanglement for different window sizes with exact solution; (b) exact error in entanglement calculations for different truncation window sizes.
  • Figure 3: Logarithmic negativity N versus time $t$ for $M=3$ and $N=30$ for the dephasing rates as marked. Ensemble dephasing is modeled by the Eq. (\ref{['eq:dephasing_master']}).
  • Figure 4: Logarithmic negativity $\cal{N}$ plotted as a function of the dephasing rate $\gamma$. The curves correspond to distinct ensemble sizes $N=\{3,10,20,30\}$ and are computed at the four magic times of the ideal protocol. (a) $t=\pi/3$. (b) $t=\pi/2$. (c) $t=2\pi/3$. (d) $t=\pi$.