Preparation and manipulation of qutrit decoherence-free subsystems

The interest in decoherence-free, or noiseless subsystems (DFS/NSs) of quantum systems is both of fundamental and practical interest. Their practical importance stems from the fact that DFSs are useful for protecting quantum information in quantum cryptography and quantum computing systems. This report provides the transformations which are compatible with a decoherence-free two-state system encoded in the product space of three physical three-state systems. The transformations are compatible with the DFS in the sense that they do not take logical states outside of the DFS/NS during the transformation. Furthermore, a proposal for a method of preparing a single logically encoded two-state system (qubit) that is immune to collective noise acting on the Hilbert space of the particles supporting it is also given. The logical qubit is comprised of three photonic 3-state systems (qutrits) and is generated by the process of spontaneous parametric down-conversion. The states are constructed using linear optical elements along with three down-conversion sources, and are deemed successful by the simultaneous detection of six events.