Long-distance high-fidelity continuous-variable quantum key distribution with non-Gaussian operations: An exact closed form solution

Abstract

In this paper, we derive a closed-form expression for the output state of a CV-QKD protocol in the presence of zero-photon catalysis (ZPC) and a quantum scissor (QS). Then, based on this closed-form solution, we use a direct search algorithm to find the appropriate values of input state and QS parameters, which considerably enhance the range and the fidelity of a CV-QKD protocol. In the special case of pure loss channel, the largest range of the protocol is only 6.5% less than the fundamental limit of repeaterless quantum communication. In addition, examination of the protocol for different values of excess noise, reveals that there is a trade-off between range and fidelity, and a high value of fidelity can be obtained at the cost of a slight reduction in protocol range.