{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/exploring-the-quantum-capacity-of-a-gaussian","title":"Exploring the quantum capacity of a Gaussian random displacement channel using Gottesman-Kitaev-Preskill codes and maximum likelihood decoding","arxiv_id":"2411.04277","date":"2024-11-06","proceeding":null,"authors":["Mao Lin","Kyungjoo Noh"],"abstract":"Determining the quantum capacity of a noisy quantum channel is an important problem in the field of quantum communication theory. In this work, we consider the Gaussian random displacement channel $N_{\\sigma}$, a type of bosonic Gaussian channels relevant in various bosonic quantum information processing systems. In particular, we attempt to make progress on the problem of determining the quantum capacity of a Gaussian random displacement channel by analyzing the error-correction performance of several families of multi-mode Gottesman-Kitaev-Preskill (GKP) codes. In doing so we analyze the surface-square GKP codes using an efficient and exact maximum likelihood decoder (MLD) up to a large code distance of $d=39$. We find that the error threshold of the surface-square GKP code is remarkably close to $\\sigma=1/\\sqrt{e}\\simeq 0.6065$ at which the best-known lower bound of the quantum capacity of $N_{\\sigma}$ vanishes. We also analyze the performance of color-hexagonal GKP codes up to a code distance of $d=13$ using a tensor-network decoder serving as an approximate MLD. By focusing on multi-mode GKP codes that encode just one logical qubit over multiple bosonic modes, we show that GKP codes can achieve non-zero quantum state transmission rates for a Gaussian random displacement channel $N_{\\sigma}$ at larger values of $\\sigma$ than previously demonstrated. Thus our work reduces the gap between the quantum communication theoretic bounds and the performance of explicit bosonic quantum error-correcting codes in regards to the quantum capacity of a Gaussian random displacement channel.","url_abs":"https://arxiv.org/abs/2411.04277v2","url_pdf":"https://arxiv.org/pdf/2411.04277v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"exploring-the-quantum-capacity-of-a-gaussian","repo_url":"https://github.com/amazon-science/latticealgorithms.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}