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.
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Publication details
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Cite this article
APA 7
Koudia, S., Kadid, S., Chatzinotas, S., & Debbah, M. (2026). Joint GKP Encoding for GHZ States Transmission over Bosonic Quantum MIMO Channels. https://omanscience.com/en/articles/joint-gkp-encoding-for-ghz-states-transmission-over-bosonic-quantum-mimo-channels
MLA 9
Koudia, Seid, et al. "Joint GKP Encoding for GHZ States Transmission over Bosonic Quantum MIMO Channels." https://omanscience.com/en/articles/joint-gkp-encoding-for-ghz-states-transmission-over-bosonic-quantum-mimo-channels.
Chicago (author–date)
Koudia, Seid, Selssabil Kadid, Symeon Chatzinotas, and Mérouane Debbah. 2026. "Joint GKP Encoding for GHZ States Transmission over Bosonic Quantum MIMO Channels." https://omanscience.com/en/articles/joint-gkp-encoding-for-ghz-states-transmission-over-bosonic-quantum-mimo-channels.
Harvard
Koudia, S., Kadid, S., Chatzinotas, S. and Debbah, M. (2026) 'Joint GKP Encoding for GHZ States Transmission over Bosonic Quantum MIMO Channels', Available at: https://omanscience.com/en/articles/joint-gkp-encoding-for-ghz-states-transmission-over-bosonic-quantum-mimo-channels.
Vancouver
Koudia S, Kadid S, Chatzinotas S, Debbah M. Joint GKP Encoding for GHZ States Transmission over Bosonic Quantum MIMO Channels. https://omanscience.com/en/articles/joint-gkp-encoding-for-ghz-states-transmission-over-bosonic-quantum-mimo-channels
IEEE
S. Koudia, S. Kadid, S. Chatzinotas, and M. Debbah, "Joint GKP Encoding for GHZ States Transmission over Bosonic Quantum MIMO Channels," https://omanscience.com/en/articles/joint-gkp-encoding-for-ghz-states-transmission-over-bosonic-quantum-mimo-channels.