Figure 7

(a) Working principle of an heralded qubit amplifier based on teleportation^34,35,36. A successful heralding is indicated with a flag. It notifies that a photon at the input port, \(a\), of the qubit amplifier was teleported to a photon at its output port, \(c\). For this, the qubit amplifier first generates a bipartite entangled state, \({\rho }_{bc}\), and then measures the signals in modes \(a\) and \(b\) with a BSM. In doing so, the state of the photon at mode \(a\) is teleported to that at mode \(c\) up to a unitary rotation. The only difference between the qubit amplifiers proposed in^34,35,36 is the mechanism to generate the entangled states \({\rho }_{bc}\). See the main text for further details. (b) Linear-optics BSM. The input states in modes \(a\) and \(b\) interfere at a 50:50 beamsplitter (BS). A polarizing BS (PBS) located at each output port of the BS separates vertically and horizontally polarised photons. Here we shall assume that all detectors are PNR detectors. A successful BSM corresponds to detecting two photons with orthogonal polarizations, i.e., only when exactly two detectors record one input photon each for any of the following photodetector pairs: \(\left({D}_{h},{D}_{v}\right)\), \(({D}_{h},{\widetilde{D}}_{v})\), \(({\widetilde{D}}_{h},{D}_{v})\) or \(({\widetilde{D}}_{h},{\widetilde{D}}_{v})\). (c) Scheme introduced in³⁵ to generate \({\rho }_{bc}\). A light source emits horizontally (vertically) polarised single-photons \({\rho }_{{\rm{s}}{\rm{i}}{\rm{n}}{\rm{g}}{\rm{l}}{\rm{e}}}^{h}\) (\({\rho }_{{\rm{s}}{\rm{i}}{\rm{n}}{\rm{g}}{\rm{l}}{\rm{e}}}^{v}\)), which interfere at a PBS and then go through a BS of tunable transmittance \(t\). Two Hadamard gates, denoted by \(H\) in the figure, are used to avoid (if one disregards noise effects) that input vacuum signals at mode \(a\) can produce a successful heralding flag when the BSM is that given by (b).