Ideal Quantum Teleamplification up to a Selected Energy Cutoff Using Linear Optics

We introduce a linear optical technique that can implement ideal quantum teleamplification up to the nth Fock state, where n can be any positive integer. Here teleamplification consists of both quantum teleportation and noiseless linear amplification (NLA). This simple protocol consists of a beam splitter and an (n+1) splitter, with n ancillary photons and detection of n photons. For a given target fidelity, our technique improves success probability and physical resource costs by orders of magnitude over current alternative teleportation and NLA schemes. We show how this protocol can also be used as a loss-tolerant quantum relay for entanglement distribution and distillation.