Joint GKP Encoding for GHZ States Transmission over Bosonic Quantum MIMO Channels
Abstract
We study transmission of a Greenberger-Horne-Zeilinger (GHZ) state over nonunitary quantum multiple-input multiple-output (QuMIMO) channels using finite-energy Gottesman-Kitaev-Preskill (GKP) encoding. A coupled-mode model describes coherent mixing, mode-dependent attenuation, and Gaussian noise. The transceiver combines programmable passive meshes, quantum-limited MMSE gain, local GKP recovery, and joint classical syndrome decoding. We optimize complex-Givens lattices using instantaneous channel-state information (CSI), current singular values with channel statistics, or statistics alone. Simulations show that joint lattice shaping outperforms product GKP processing. Under coherent-basis drift, full instantaneous CSI improves GHZ-state preservation, whereas singular-value conditioned and fully statistical designs perform similarly because neither resolves the current singular frames. These findings identify singular-frame geometry as a critical resource beyond attenuation knowledge where joint GKP processing adapts the logical lattice and receiver to anisotropic bosonic noise rather than merely inverting multimode mixing.
Related
- Quantum advantage in learning single mode bosonic channels
- No information transmission through quantum channels above capacity
- Private Capacity of Quantum Channels Induced by Non-stabilizer Environmental States
- Optimal learning of covariant quantum states and channels
- Quantum de Finetti theorems for states and channels in any distance measure
BibTeX
@misc{koudia2026joint,
title = {{Joint GKP Encoding for GHZ States Transmission over Bosonic Quantum MIMO Channels}},
author = {Seid Koudia and Selssabil Kadid and Symeon Chatzinotas and Mérouane Debbah},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05992},
eprint = {2610.05992},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05992},
}
RIS
TY - UNPB
TI - Joint GKP Encoding for GHZ States Transmission over Bosonic Quantum MIMO Channels
AU - Seid Koudia
AU - Selssabil Kadid
AU - Symeon Chatzinotas
AU - Mérouane Debbah
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05992
UR - https://arxiv.org/abs/2610.05992
AB - We study transmission of a Greenberger-Horne-Zeilinger (GHZ) state over nonunitary quantum multiple-input multiple-output (QuMIMO) channels using finite-energy Gottesman-Kitaev-Preskill (GKP) encoding. A coupled-mode model describes coherent mixing, mode-dependent attenuation, and Gaussian noise. The transceiver combines programmable passive meshes, quantum-limited MMSE gain, local GKP recovery, and joint classical syndrome decoding. We optimize complex-Givens lattices using instantaneous channel-state information (CSI), current singular values with channel statistics, or statistics alone. Simulations show that joint lattice shaping outperforms product GKP processing. Under coherent-basis drift, full instantaneous CSI improves GHZ-state preservation, whereas singular-value conditioned and fully statistical designs perform similarly because neither resolves the current singular frames. These findings identify singular-frame geometry as a critical resource beyond attenuation knowledge where joint GKP processing adapts the logical lattice and receiver to anisotropic bosonic noise rather than merely inverting multimode mixing.
ER -