I present a series of experimental and theoretical advances in the field of quantum state estimation. Techniques for measuring the quantum state of light that were originally developed for distinguishable photons fail when the particles are indistinguishable. I develop new methods for handling indistinguishability in quantum state estimation. The technique I present provides the first complete description of states of experimentally indistinguishable photons. It allows me to derive the number of parameters needed to describe an arbitrary state and to quantify distinguishability. I demonstrate its use by applying it to the measurement of the quantum polarization state of two and three-photon systems.

State characterization is optimal when no redundant information is collected about the state of the system. I present the results of the first optimal characterization of the polarization state of a two-photon system. I show an improved estimation power over the previous state of the art. I also show how the optimal measurements lead to a new description of the quantum state in terms of a discrete Wigner function.

It is often desirable to describe the quantum state of a system in terms of properties that are not themselves quantum-mechanical observables. This usually requires a full characterization of the state followed by a calculation of the properties from the parameters characterizing the state. I apply a technique that allows such properties to be determined directly, without a full characterization of the state. This allows one such property, the purity, to be determined in a single measurement, regardless of the size of the system, while the conventional method of determining purity requires a number of measurements that scales exponentially with the system size.