Oscillator-to-oscillator codes do not have a threshold

Understand

It is known that continuous variable quantum information cannot be protected against naturally occurring noise using Gaussian states and operations only.

• Noh et al.
• (PRL 125:080503, 2020) proposed bosonic oscillator-to-oscillator codes relying on non-Gaussian resource states as an alternative, and showed that these encodings can lead to a reduction of the effective error strength at the logical level as measured by the variance of the classical displacement noise channel.
• An oscillator-to-oscillator code embeds K logical bosonic modes (in an arbitrary state) into N physical modes by means of a Gaussian N-mode unitary and N-K auxiliary one-mode Gottesman-Kitaev-Preskill-states.