Asymptotically good bosonic Fock state codes

TL;DR

This paper introduces asymptotically good multi-mode Fock-state codes that can correct amplitude-damping noise effectively in the large excitation limit, using a novel random classical code approach.

Contribution

It constructs new Fock-state codes that are asymptotically good against amplitude-damping noise by leveraging randomness in classical indexing and a new equivalence in error correction.

Findings

Codes protect against amplitude-damping noise with linear photon loss scaling

Random classical indexing enables bounded per-mode photon occupancy

Results extend to permutation-invariant and nuclear state codes

Abstract

We study the error-correction properties of multi-mode Fock-state codes under amplitude-damping (AD) noise, focusing on the asymptotic regime in which the total excitation of the code states grows without limit and the number of photon losses induced by the noise scales linearly with it. In this setting, existing code families, which correct only sublinearly many photon losses, do not protect against amplitude-damping (AD) noise with a constant loss parameter. We address this gap by constructing asymptotically good Fock-state codes relying on random classical codes in the discrete simplex. Our approach is based on a new equivalence between approximate correction for the AD channel and exact or approximate correction of sufficiently many photon losses under a truncated AD channel. Unlike many standard constructions of random quantum codes, our construction introduces randomness through the underlying classical indexing structure. Randomization also enables another desirable feature: bounded per-mode occupancy, which limits the number of photons in any individual mode and thereby increases the coherence lifetime of the code states. Finally, via a relation between Fock-state codes and permutation-invariant codes, our results also yield asymptotically good families of qudit permutation-invariant codes as well as codes in monolithic nuclear state spaces.