Exploring the quantum capacity of a Gaussian random displacement channel using Gottesman-Kitaev-Preskill codes and maximum likelihood decoding · arXivDesk
2411.04277Nov 6, 20244.4 + 11.1 pages, 3+4 figures. Correct labels in Fig. 3 and added two sections in deriving hashing bound of Pauli channels and the lower bound of the quantum capacity for a Gaussian random displacement channel
Exploring the quantum capacity of a Gaussian random displacement channel using Gottesman-Kitaev-Preskill codes and maximum likelihood decoding
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 Nσ, 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 σ=1/e≃0.6065
Nearby in the stack
at which the best-known lower bound of the quantum capacity of
Nσ
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
Nσ
at larger values of
σ
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.
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