Composable security of unidimensional continuous-variable quantum key distribution

We investigate the composable security of unidimensional continuous-variable quantum key distribution (UCVQKD) protocol in generally phase-sensitive channel; the UCVQKD protocol is based on the Gaussian modulation of a single quadrature of the coherent state of light, aiming to provide a simple implementation of key distribution compared to the symmetrically modulated Gaussian coherent-state protocols. This protocol neglects the necessity in one of the quadrature modulations in coherent states and hence reduces the system complexity. To clarify the influence of finite-size effect and the cost of performance degeneration, we establish the relationship of the balanced parameters of the unmodulated quadrature and estimate the precise secure region. Subsequently, we illustrate the composable security of the UCVQKD protocol against collective attacks and achieve the tightest bound of the UCVQKD protocol. Numerical simulations show the asymptotic secret key rate of the UCVQKD protocol, together with the symmetrically modulated Gaussian coherent-state protocols.