Environment-assisted quantum transduction with GKP states

Quantum transducers convert quantum signals between physically distinct carriers, enabling quantum information exchange across multiple platforms in quantum networks. For quantum transduction between two bosonic modes, the direct transduction without shared entanglement or classical communication typically requires a conversion efficiency exceeding 0.5 which is challenging in current experiments. We propose the environment-assisted quantum transduction scheme to overcome this stringent requirement. Without internal losses, added noises to the transduction channel 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 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 we find that high fidelity quantum transduction remains achievable with GKP states at the few-photon level.