Practical, High-Speed, Gaussian Modulated Coherent State Continuous Variable Quantum Key Distribution with Real-Time Post Processing

Abstract

Quantum key distribution is proven to achieve unconditional security based on the laws of quantum physics. Quantum key distribution was originally proposed using discrete variables. Later, continuous-variable quantum key distribution has been introduced. Continuous variable quantum key distribution with Gaussian modulated coherent states has gained interest due to its security and compatibility with classical coherent optical fibre networks. For successful system deployment, it is essential to implement practical, high-speed, systems that distils secret keys in real-time. Most existing demonstrations of continuous variable key distribution systems utilise bulky laboratory equipment such as arbitrary waveform generators and oscilloscopes to generate and record signals. To build practical systems that can be deployed in the field, it is important to investigate the use of commercially available digital-to-analogue converters and analogue-to-digital to converters for data generation at the sender and real-time data recording at the receiver respectively. Moreover, most demonstrations of Gaussian modulated coherent state continuous variable quantum key distribution to date, estimate the secret key rates without real secret key distillation. Therefore, it is crucial to build fully functional, practical systems with high-speed post processing toolchains that can distil secret keys in real-time. In this thesis, a Gaussian modulated coherent state continuous variable quantum key distribution system with a repetition rate of 50 MHz, the highest repetition rate for a similar practical system, is presented. This fully functional system consists of front-end optical hardware and the back-end real-time post processing toolchain. A real-time parameter monitoring software module is developed, which continuously measures excess noise and detects unstable operation immediately. With the measured excess noise, asymptotic key rates of 9.1 Mb/s, 6.8 Mb/s, 5.2 Mb/s, 3.8 Mb/s, 2.0 Mb/s, and 1.1 Mb/s are estimated for transmission distances of 15 km, 20 km, 25 km, 30 km, 40 km, and 50 km respectively. These are record asymptotic key rates for similar practical Gaussian modulated coherent state continuous variable quantum key distribution systems. Slice reconciliation is applied to convert continuous variables into bit strings within continuous variable quantum key distribution systems. In Gaussian modulated coherent state continuous variable quantum key distribution systems, even at moderately high signal-to-noise ratios observed after metropolitan transmission distances, the bit error rates remain high. High bit error rates result in high computational complexity for error correction. Most of the bit errors occur at the decision points applied within the Gaussian distribution of data during the slice reconciliation procedure. Therefore, in this thesis, for the first time, ‘guard bands’ are applied around these decision points, so that data lying within the guard bands can be discarded. This lowers the overall bit error rates at the expense of removing a small portion of the data blocks. An optimisation method to determine the widths of guard bands that maximises the final secret key rates is also presented. For instance, with optimised slicing, secret key rates (under finite-size effects and after privacy amplification) of 6.1 Mb/s, 4.9 Mb/s, and 3.7 Mb/s are achieved for transmission distances of 20 km, 25 km, and 30 km. These are record secret key rates for practical Gaussian modulated coherent state continuous variable quantum key distribution systems. Post processing for quantum key distribution consists of error correction and privacy amplification. Here, low density parity check codes are used for error correction, and fast Fourier transform-based method with circulant matrices are used for privacy amplification. Most previous studies on post processing focus on either error correction or privacy amplification without integrating them into a full continuous variable quantum key distribution system. Here, the back-end post processing toolchain is integrated with the complete system to distil secret keys in real-time. To achieve real-time post processing, the throughput rates of error correction and privacy amplification must support the raw asymptotic key rates achieved from the continuous variable quantum key distribution system. The asymptotic key rates achieved from the system presented here are on the order of a few Mb/s. Post processing speeds up to a few Gb/s have been achieved using graphical processing units and field programmable gate arrays in previous studies. However, in this practical system, more user-friendly central processing units are used. To achieve error correction speeds in the order of a few Mb/s, software techniques such as multi-threading and sparse matrix storage for parity check matrices are utilised on the central processing unit. Error correction speeds of up to 9.6 Mb/s have been achieved here. With the fast Fourier transform based privacy amplification method, throughput rates up to 9.3 Mb/s have been realised. These post processing speeds can support the record real-time secret key distillation for transmission distances ranging from 15 km to 50 km achieved from this system.