Superposition-preserving photon-number amplifier
Gunnar G. Bjork, Jonas Söderholm, Anders L. Karlsson · Physical Review A · 1998
We analyze a pure-state photon-number amplifier (PNA), i.e., a device that performs the action $|{\ensuremath{\psi}}_{\mathrm{in}}〉={\ensuremath{\sum}}_{l}{c}_{l}|l\stackrel{\ensuremath{\rightarrow}}{〉}|{\ensuremath{\psi}}_{\mathrm{out}}〉={\ensuremath{\sum}}_{l}{c}_{l}|\mathrm{Gl}〉,$ where $G$ is a positive integer. We derive expressions for the fidelity of a finite internal state PNA and demonstrate that the amplifier fidelity, i.e., the similarity between the obtained and the desired output state can be made to approach unity. Finally we outline a systematic procedure to find the Hamiltonian for any finite Hilbert-space PNA and compute the Hamiltonian for a simple but nontrivial PNA.