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Quantum mechanics of adding and subtracting a photon

We have witnessed proliferate growth in theoretical and experimental efforts to understand and control physical systems in a quantum level. In a quantum optics laboratory, Gaussian states, whose phase properties are described by Gaussian probability-like functions, were generated but there was some limitation to use them for various tasks of quantum information processing. There have been suggestions and realisations to engineer the quantum state by subtracting or adding single photons from/to a Gaussian field. It is also possible to test fundamental quantum theories using these techniques. We discuss various issues in subtraction and addition of single photons.