Eight-port homodyne detector: The effect of imperfections on quantum random-number generation and on detection of quadratures

The eight-port homodyne detector is an optical circuit designed to perform the monitoring of two quadratures field, signal. By using quantum Bose fields and stochastic calculus, we give a complete description this apparatus, when used as quadrature in continuous time. We can treat either travelling waves circuit, observables involved detection part: couples photodiodes, postprocessing output currents. analysis includes imperfections, such not perfectly balanced beam splitters, efficiency, electronic noise, phase intensity noise laser acting local oscillator; last modelled by mixtures field coherent states statistical operator component. Due time, process its full probability distribution obtained. When sampled at discrete times, be reduced mode operators, but price having random which contain also oscillator. Consequently, oscillator has very different effect on results with respect additive components. As application, problem secure number generation considered, based shot noise. rate bits that generated quantified min-entropy; possibility classical side information taken into account suitable conditional min-entropies. final depends parts apparatus are considered ones exposed intervention intruder. In some experimentally realistic situations, entropy losses computed.