Asymptotically good bosonic Fock state codes

Dor Elimelech; Arda Aydin; Alexander Barg

doi:10.22331/q-2026-10-20-2240

Asymptotically good bosonic Fock state codes

Dor Elimelech^1,2, Arda Aydin², and Alexander Barg^2,1,3

¹Joint Center for Quantum Information and Computer Science (QuICS), UMD/NIST
²Institute for Systems Research, University of Maryland, College Park, MD 20742
³Department of ECE, University of Maryland, College Park, MD 20742

Published:	2026-10-20, volume 10, page 2240
Editor:	Carlo Beenakker
Eprint:	arXiv:2603.15190v3
Doi:	https://doi.org/10.22331/q-2026-10-20-2240
Citation:	Quantum 10, 2240 (2026).

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Abstract

We study the error-correction properties of multi-mode Fock-state codes under amplitude-damping (AD) noise, focusing on the asymptotic regime in which the total excitation of the code states grows without limit and the number of photon losses induced by the noise scales linearly with it. In this setting, existing code families, which correct only sublinearly many photon losses, do not protect against amplitude-damping (AD) noise with a constant loss parameter. As our main result, we address this gap by constructing asymptotically good Fock-state codes relying on random classical codes in the discrete simplex. Unlike many standard constructions of random quantum codes, our construction introduces randomness through the underlying classical indexing structure. Randomization also enables another desirable feature: bounded per-mode occupancy, which limits the number of photons in any individual mode and thereby increases the coherence lifetime of the code states. Finally, via a relation between Fock-state codes and permutation-invariant codes, our results also yield asymptotically good families of qudit permutation-invariant codes as well as codes in monolithic nuclear state spaces.

► BibTeX data

@article{Elimelech2026asymptoticallygood,
  doi = {10.22331/q-2026-10-20-2240},
  url = {https://doi.org/10.22331/q-2026-10-20-2240},
  title = {Asymptotically good bosonic {F}ock state codes},
  author = {Elimelech, Dor and Aydin, Arda and Barg, Alexander},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2240},
  month = oct,
  year = {2026}
}

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Cited by

[1] Dor Elimelech, Victor V. Albert, and Alexander Barg, "Theory of approximate quantum error correction and the error-set model", arXiv:2607.22995, (2026).

[2] Varin Sikand and Andrew Nemec, "Quantum Anonymous Secret Sharing with Permutation Invariant Codes", arXiv:2604.27284, (2026).

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