Postselection strategies for CV-QKD protocols with phase-shift keying modulation

Abstract

Quantum Key Distribution, or short QKD, aims to establish a secure key withoutmaking any additional assumptions about the abilities or computational power of an adversary who is only limited by the laws of nature. The process of finding a mathematical expression for, or at least a lower bound on, the secure keyrate of some QKD protocol, given relevant system parameters, is called securityproof. In this thesis, we use a recent numerical security proof technique to examine different post selection strategies for continuous-variable quantum key distribution(CV-QKD) protocols with quadrature phase-shift keying modulation and four or eight signal states. CV-QKD protocols use coherent states to encode information and measure the field-quadrature components by homodyne or heterodyne detection. The basic idea of the used numerical security proof technique is to solve thekey rate finding problem in a two-step process. In the first step, the problem is solved approximately, using a numerical algorithm, which yields an upper bound on the secure key rate. This is followed by step two, where the obtained upperbound is converted into a lower bound, using a sequence of theorems and taking numerical errors into account. Postselection aims to increase the secure key rate by removing those parts of the key, where a potential adversary might have gained more information than the communicating parties. The investigations are carried out both for the untrusted ideal and the trusted non-ideal detector scenario and we provide novel analytical results for the operators related to the postselection map.For four-state protocols, we demonstrate that a new cross-shaped postselectionstrategy out performs the state-of-the-art radial postselection scheme clearly in regions of medium to high transmission distances and medium to high values of noise and performs comparable to a more complicated radial&angular scheme. As the error-correction phase is a known bottleneck for many real QKD systems, we examined the secure key rate when a large fraction of the raw key is removed by postselection. We observe that a smart choice of the postselection strategy can increase the key rate while lowering the raw key rate, hence the computational effort in the error-correction phase. One can think this even further: For cross-shaped postselection we showed that the secure key rate is roughly 80% of the secure keyrate without postselection when only 20% of the raw key passes the postselection.For high noise levels this can be increased even further. The cross-shaped post-selection strategy can easily be implemented in the data processing of both new and existing CV-QKD systems, hence can increase the achievable secure key rate significantly. Furthermore, we examined the radial&angular postselection strategy which combines the advantages of the radial postselection scheme for low transmission distances and those of the cross-shaped postselection scheme for medium and high transmission distances on the cost of higher complexity.Additionally, we examine an eight-state phase-shift keying protocol and compare the obtained key rates to the key rates for the four-state protocol and investigate a radial postselection scheme. We observe that the 8PSK protocol yields higher secure key rates and reaches higher maximal achievable transmission distances than a QPSK protocol with a comparable postselection strategy, in particular for medium to high values of excess noise. Furthermore, we explore the relation between the achievable secure key rate and the probability to pass the postselectionphase for various noise-levels and two different practically relevant reconciliation efficiencies. This leads to similar strategies as found for the QPSK protocols to reduce the raw key rate significantly while decreasing the secure key rate only moderately. For very high values of excess noise, the raw key rate can be increased further compared to the key rate achieved without performing postselection whileremoving a large fraction of the raw key rate.