In this thesis, we address critical problems on implementation of quantum key distribution (QKD), and two-qubit unitary estimation using linear optics. One of the most serious issues for practical implementation of the traditional QKD protocol is loss of alignment of shared reference-frame axes between communication parties. Reference-frame-independent quantum key distribution (rfi-QKD) is a protocol that circumvents this issue. Chapter 3 presents an experimental realisation of the rfi-QKD protocol that harnesses polarisations of photonic qubits for key exchange over a telecom polarisation-maintaining fibre (PMF). We have tested the rfi-QKD protocol and demonstrated its robustness for the typical environment in which the PMF would be deployed, including a unique feature of the system that allows the key exchange to recover itself after a period of disturbance. Following on from this work, we propose an ideal implementation of the rfi-QKD protocol configured as a communication between a client and a server, which provides a real prospect for putting this quantum technology into practical use. Next we present work on developing a two-qubit quantum processor, a resource for simulating two-qubit unitary transformation. This work includes theoretical and experimental parts, as well as a complete scheme for bulk-optical implementation. In chapter 4, theoretical work provides both an abstract technique and a linear-optical model for constructing an arbitrary two-qubit gate by implementing a linear combination of quantum operations. This work builds upon a method for adding control to an arbitrary unknown quantum operations in X.-Q. Zhou et al, Nature Communications 2, 413 {2011}. Then, we propose a reconfigurable circuit that harnesses two photons and simple linear-optical elements for implementing a system that can be used as a tool kit for simulating a two-qubit unitary evolution when the inputs are known and in the form of product states. A subset of the complete bulk optical scheme has been experimentally demonstrated and reported in chapter 5.