Theoretical issues in quantum information technologies

Quantum theory offers a glimpse into a world very different from the world that we daily experience. Quantum particles behave in ways that defy common sense. An important question is whether one can use the quantum aspect of nature to gain a technological advantage over the classical world. The answer is a resounding yes, and quantum information technologies attempt to exploit these quantum properties. Quantum information technologies offer advantages in computation, cryptography, and precision measurements. In this thesis, I explore theoretical and physical challenges to implementing these techniques. I first explore the possibility of using decoherence-free subspaces for the storage of quantum information. I approach the question theoretically and show that decoherence-free subspaces exist for a large array of collective errors. I also approach the question from a physical standpoint and show how one can design a quantum computer using trapped ions that exploits a decoherence-free subspace to avoid common errors in ion traps. I then examine whether or not is possible to implement the solid state analogue of an ion trap quantum computer. Specifically, I explore the possibility of entangling quantum dots indirectly via the quantized motion of a rod to which both dots are attached. I then study the effects of defective oracles on continuous-time quantum algorithms. In particular, I show that the quantum search algorithm is quite sensitive to oracles with phase errors, while other algorithms are quite robust to the same noise. I then show how to deterministically produce N photons from N atoms in a cavity. N-photon states can be used for quantum computation, quantum cryptography and precision measurements. Thus, this thesis explores many aspects of quantum information technologies within the context of both reasonable physical models and fundamental theoretical questions.