Squeezed Vacuum State Approximation of Discrete Unidimensional Coherent State Constellations

Recent research on QKD Protocols has focused on discrete modulation schemes for continuous-variable systems, which is a new paradigm in therms of security proof methodologies. Common security proof methodology consists on establishing an equivalent entangled based protocol, which requires the discrete modulated states purification. Here we show how one could approximate the constellation ensemble by a (pure) squeezed vacuum state. We use the quantum fidelity distance measure to calculate the squeezing factor and show that low quadrature modulation variance enables high fidelity between the ensemble and the approximated state.