Abstract: The secure key rate of a QKD protocol can be expressed as a convex minimization over all the states compatible with observed statistics. Recently developed numerical methods allow one to reliably and tightly solve this minimization when the states are finite dimensional. However, when the states are infinite dimensional, it is no longer possible to directly solve the minimization. Fortunately, for many discrete-variable protocols, the problem can be mapped into finite dimensions using squashing models or the flag-state squasher. However, these squashing approaches do not seem applicable to continuous-variable (CV) protocols. We introduce a dimension reduction method which connects the infinite-dimensional description of protocols to a tractable finite-dimensional formulation, enabling the calculation of secure key rates for general protocols in infinite-dimensional Hilbert spaces. We apply this method to obtain asymptotic key rates for discrete-modulated continuous-variable QKD protocols, which are of practical significance due to their experimental simplicity and potential for large-scale deployment in quantum-secured networks. Importantly, our security proof does not require the photon-number cutoff assumption relied upon in previous works. We also demonstrate that our method can provide practical advantages over the flag-state squasher when applied to discrete-variable protocols.
[due to some technical problem, the first few minutes of the talk were not recorded. We are sorry for that.]