Passive environment-assisted quantum information transfer.

A bosonic pure-loss channel, modeled as transmission through a beam splitter with a vacuum input state at the dark port, has zero quantum capacity when transmissivity is below 50%. By using passive environment assistance—selecting an appropriate input state for the dark port—quantum communication through the channel can be enhanced. Although ideal Gottesman-Kitaev-Preskill (GKP) states enable perfect quantum information transmission at arbitrarily small transmissivity, they are challenging to realize experimentally. Consequently, we explore alternative non-Gaussian environment states, such as Fock states, cat states, and squeezed cat states, for the dark port input. We numerically determine the optimal encoding and decoding under photon number constraints. Additionally, we explore other bosonic channels and scenarios involving multiple modes.