Quantum interferences reconstruction with low homodyne detection efficiency
Martina Esposito, Francesco Randi, Kelvin Titimbo, Georgios Kourousias, Alessio Curri, Roberto Floreanini, Fulvio Parmigiani, Daniele Fausti, Klaus Zimmermann, Fabio Benatti · EPJ Quantum Technology · 2016
Optical homodyne tomography consists in reconstructing the quantum state of an optical field from repeated measurements of its amplitude at different field phases (homodyne data). The experimental noise, which unavoidably affects the homodyne data, leads to a detection efficiency $\eta 0.5$ ) below which quantum features, like quantum interferences, cannot be retrieved. Here, by numerical experiments, we demonstrate that quantum interferences can be effectively reconstructed also for low homodyne detection efficiency. In particular, we address the challenging case of a Schrödinger cat state and test the minimax and adaptive Wigner function reconstruction technique by processing homodyne data distributed according to the chosen state but with an efficiency $\eta< 0.5$ . By numerically reproducing the Schrödinger’s cat interference pattern, we give evidence that quantum state reconstruction is actually possible in these conditions, and provide a guideline for handling optical tomography based on homodyne data collected by low efficiency detectors.