  Quantum transducers convert quantum signals from one carrier to another
through hybrid interfaces of physical systems. For a quantum transducer between
two bosonic modes, direct quantum transduction without shared entanglement or
classical communication typically requires a conversion efficiency exceeding
0.5 which is challenging for current experiments. We propose the passive
environment-assisted quantum transduction to overcome this stringent
requirement. Without internal losses, the quantum transducer realizes a beam
splitter unitary between two modes. The added noises to the transduction
process from mode 1 to mode 2 is determined by the initial state of mode 2,
which can be engineered to enhance the transduction performance. We find that
by choosing the ideal Gottesman-Kitaev-Preskill (GKP) states as the initial
states of both modes, perfect quantum transduction can be achieved at
arbitrarily low conversion efficiencies. In practice, it is crucial to also
consider the finite energy constraints and high fidelity quantum transduction
remains achievable with GKP states at the few-photon level.
