Bosonic Loss Codes with Bounded Occupation
Abstract
We study Fock-state codes on q bosonic modes, with total excitation N and at most B excitations per mode, that exactly correct every pattern of at most δN photon losses, for q proportional to N. For every fixed cap B and every ratio q/N>1/B, we prove explicit achievable rates, positive for all sufficiently small δ>0, in logical qubits per excitation. At B=2 and q=N, the rate is positive for every δ<0.1355 and is about $0.281$ at δ=0.1, compared with the previously established exact-code qutrit rate of about $0.275$. We also give an explicit upper bound on the dimension of every such exact code, including degenerate codes. For the pure-loss channel truncated to at most δN losses and renormalized, we obtain approximate codes with exponentially small worst-case error. When the loss probability is positive and at most 1/(B+1), they improve our positive exact-code rate bounds; at B=2, q=N, and loss probability $0.1$, they remain positive up to δ≈0.158.
Related
- Optimal two-mode bosonic loss codes from finite group symmetry
- Bosonic codes from compact phase spaces
- Asymptotically good bosonic Fock state codes
- Improved lower bound for the two-way-assisted quantum capacity of the bosonic thermal-loss channel
- Photon-stimulated decay of χ-matched ancillas causes unheralded bit flips in bosonic codes
BibTeX
@misc{kreindel2026bosonic,
title = {{Bosonic Loss Codes with Bounded Occupation}},
author = {Avraham Kreindel and Aryeh Lev Zabokritskiy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34411},
eprint = {2610.34411},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34411},
}
RIS
TY - UNPB
TI - Bosonic Loss Codes with Bounded Occupation
AU - Avraham Kreindel
AU - Aryeh Lev Zabokritskiy
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34411
UR - https://arxiv.org/abs/2610.34411
AB - We study Fock-state codes on q bosonic modes, with total excitation N and at most B excitations per mode, that exactly correct every pattern of at most δN photon losses, for q proportional to N. For every fixed cap B and every ratio q/N>1/B, we prove explicit achievable rates, positive for all sufficiently small δ>0, in logical qubits per excitation. At B=2 and q=N, the rate is positive for every δ<0.1355 and is about $0.281$ at δ=0.1, compared with the previously established exact-code qutrit rate of about $0.275$. We also give an explicit upper bound on the dimension of every such exact code, including degenerate codes. For the pure-loss channel truncated to at most δN losses and renormalized, we obtain approximate codes with exponentially small worst-case error. When the loss probability is positive and at most 1/(B+1), they improve our positive exact-code rate bounds; at B=2, q=N, and loss probability $0.1$, they remain positive up to δ≈0.158.
ER -