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Optical coherent states are classical light fields with high purity, and areessential carriers of information in optical networks. If these states could becontrolled in the quantum regime, allowing for their quantum superposition(referred to as a Schr\"odinger cat state), then novel quantum-enhancedfunctions such as coherent-state quantum computing (CSQC), quantum metrology,and a quantum repeater could be realized in the networks. Optical cat statesare now routinely generated in the laboratories. An important next challenge isto use them for implementing the aforementioned functions. Here we demonstratea basic CSQC protocol, where a cat state is used as an entanglement resourcefor teleporting a coherent state with an amplitude gain. We also show how thiscan be extended to a loss-tolerant quantum relay of multi-ary phase-shift keyedcoherent states. These protocols could be useful both in optical and quantumcommunications.

Quantum tele-amplification with a continuous variable superposition state