Amplification of a polarized single-photon state and determination of resulting polarization correlations

The photon statistics of a single spatial mode of the optical field (including the two polarization states) resulting from a single-photon state undergoing unsaturated amplification by a two-level medium are derived. Results are compared with those for an idealized noiseless linear amplifier and a conventional quantum-noise-limited amplifier in the limit of no gain. When the amplified field is divided for detection of different polarization states, distinctive polarization biases and correlations are evident on average when the polarization of the input state is constant. However, the results are insufficient to determine the initial polarization state based on a single measurement. If one must average over two orthogonally polarized input states (e.g., an incoherent mixture of either linearly or circularly polarized initial states) as required in the absence of hidden variable information in an Einstein–Podolsky-Rosen experiment, the distinctions are completely erased.