Although mathematical cryptography has been widely used, its security has only been proven under certain assumptions such as the computational power of opponents. As an alternative, quantum communication, in particular quantum key distribution (QKD) does not require unproven assumptions and can achieve unconditional security. However, the key-generation rate of practical QKD systems is limited by device imperfections, excess noise from the quantum channel, a limited rate of true random-number generation, limited rate of quantum entanglement preparation, and/or high complexity of post-processing. This dissertation contributes to improved performance of quantum communication systems. First, it proposes a new continuous-variable QKD (CVQKD) protocol that loosens the efficiency requirement on post-processing, a bottleneck for long-distance CVQKD systems. It also demonstrates an experimental implementation of the proposed protocol. To allow for future higher rate implementation, the CVQKD experiment uses a continuous-wave local oscillator (CWLO). The excess noise caused by guided acoustic-wave Brillioun scattering (GAWBS) is avoided by a frequency-shift scheme. The statistical distribution of GAWBS noise is characterized by quantum tomography. Measurements show Gaussian statistics with 55 dB of dynamic range, which validate efficient security calculations used in the proposed CVQKD protocol. True random numbers are required in quantum and classical cryptography. A second contribution of this thesis is that it experimentally demonstrates an ultrafast quantum random-number generator (QRNG) based on amplified spontaneous emission (ASE). Random numbers are produced by a multi-mode photon counting measurement on ASE light. The performance of the QRNG is analyzed with quantum information theory and tested with NIST standard random-number test. The QRNG experiment demonstrates a random-number generation rate at 20 Gbit/s. A theoretical study identifies show fundamental limits for such QRNGs. Quantum entanglement produced in nonlinear optical processes can help to increase quantum communication distance. A third contribution is research of the nonlinear optics of graphene, a novel 2D material with unconventional physical properties. Based on a quantum-dynamical model, the optical response of graphene is derived, showing a link between the complex linear optical conductivity and the decoherence. Nonlinear optical response, in particular four-wave mixing, is studied for the first time. The theory predicts saturation effects in graphene and relates the saturation threshold to phenomenologically model ultrafast decoherence and carrier relaxation in graphene. Experimental efforts towards validation of this theory are discussed.