This chapter examines the use of photon ensembles for quantum computing. It opens with a primer on photons, normal modes, and both linear and nonlinear optics. The discussion then advances to the technologies employed in generating and detecting single photons, followed by methods of qubit encoding and initialization. Subsequently, the focus shifts to qubit control, detailing the execution of single-qubit gates using linear optical elements and the Knill–Laflamme–Milburn (KLM) protocol for two-qubit gates. While the textbook predominantly centers on the circuit model, alternative models of quantum computing – specifically, one-way quantum computing and continuous-variable quantum computing – and their optical implementations are introduced. Additionally, it outlines the primary sources of noise affecting these systems. The chapter wraps up with a reflection on the comparative benefits and limitations of optical quantum computing.

Chapter devoted to the basic quantum properties of entanglement and separability. Introduces the Schmidt decomposition for pure states and the positive partial transpose criterion for mixed states as entanglement witnesses. Introduces the famous Einstein–Podolsky–Rosen paradox and its implementation in terms of qubits, then the Bell inequality, quickly reviewing the experimental demonstrations that quantum mechanics violates this inequality. Gives examples of the use of entanglement in a quantum algorithm to accelerate an information task, namely a database search (Grover algorithm) and the possibility of teleportation of a quantum state.

We spend the last chapter using the learned quantum mechanical tool set to examine two current research topics that are extensions of some of the examples of quantum mechanics studied in the text. We examine quantum mechanical forces on atoms and quantum information processing, which both have important connections to Stern-Gerlach spin-1/2 experiments and to resonant atom-light interactions

In this final chapter, we focus more on quantum information and quantum computing applications of atomic ensembles. We first examine ways of implementing continuous variables in quantum information processing using atomic ensembles, based on the Holstein--Primakoff approximation. Methods to perform quantum teleportation using this method, and some seminal experiments using this approach are introduced. We then introduce other approaches not based on the Holstein--Primakoff approximation to represent quantum information, namely the spinor quantum computing scheme. After showing a simple example of how such a scheme works with Deutsch's algorithm, we describe how adiabatic quantum computing can be performed, which displays the key feature of quantum error suppression.