We propose a long-distance continuous-variable quantum key distribution (CVQKD) with a four-state protocol using non-Gaussian state-discrimination detection. A photon subtraction operation, which is deployed at the transmitter, is used for splitting the signal required for generating the non-Gaussian operation to lengthen the maximum transmission distance of the CVQKD. Whereby an improved statediscrimination detector, which can be deemed as an optimized quantum measurement that allows the discrimination of nonorthogonal coherent states beating the standard quantum limit, is applied at the receiver to codetermine the measurement result with the conventional coherent detector. By tactfully exploiting the multiplexing technique, the resulting signals can be simultaneously transmitted through an untrusted quantum channel, and subsequently sent to the state-discrimination detector and coherent detector, respectively. Security analysis shows that the proposed scheme can lengthen the maximum transmission distance up to hundreds of kilometers. Furthermore, by taking the finite-size effect and composable security into account we obtain the tightest bound of the secure distance, which is more practical than that obtained in the asymptotic limit.is relatively hard to design and implement. Fortunately, there exists another way to solve the problem, that is, using discrete modulation such as the four-state CVQKD protocol, proposed by Leverrier et al [13]. This discretely modulated CVQKD generates four nonorthogonal coherent states and exploits the sign of the measured quadrature of each state to encode information rather than using the quadraturex orp itself. This is the reason that the sign of the measured quadrature is already the discrete value to which the most excellent error-correcting codes are suitable even at very low SNR. Consequently, the four-state CVQKD protocol has the merits of both high reconciliation efficiency in the long-distance transmission and the security proof of CVQKD so that it could improve the maximal transmission distance of CVQKD.Currently, photon-subtraction operation, which is a kind of non-Gaussian operation in essence, has been demonstrated theoretically and experimentally to extend the transmission distance of the CVQKD using two-mode entangled states [23][24][25] due to the fact that a suitable photon-subtraction operation would increase the entanglement degree of two-mode entangled state and thereby increase the correlation between the two output modes of two-mode entangled state. Since the entanglement-based (EB) scheme is equivalent to the prepare-and-measure (PM) one, this operation can be employed practically implemented in protocols using coherent states with existing technologies.Furthermore, although a high-speed and high-efficiency homodyne or heterodyne detector can be used effectively to measure the received quantum state, the inherent quantum uncertainty (noise) still prevents the nonorthogonal coherent states from being distinguished with perfect accuracy [26][27][28]. Even if ...

Continuous-variable quantum key distribution (CVQKD) can be integrated with thermal states for short-distance wireless quantum communications. However, its performance is usually restricted with the practical thermal noise. We propose a method to improve the security threshold of thermal-state (TS) CVQKD by employing a heralded hybrid linear amplifier (HLA) at the receiver. We find the effect of thermal noise on the HLA-involved scheme in near-and-mid infrared band or terahertz band for direct and reverse reconciliation. Numerical simulations show that the HLA-involved scheme can compensate for the detriment of thermal noise and hence increase the security threshold of TS-CVQKD. In near-and-mid infrared band, security threshold can be extended by 2.1 dB in channel loss for direct reconciliation and 1.6 dB for reverse reconciliation, whereas in terahertz band, security threshold can be slightly enhanced for the gain parameter less than 1 due to the rise in thermal noise.

We investigate the composable security of unidimensional continuous variable quantum key distribution (UCVQKD), which 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 modulation 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.

No abstract