Semigroup techniques for the efficient classical simulation of optical quantum information

A framework to describe a broad class of physical operations (including unitary transformations, dissipation, noise, and measurement) in a quantum optics experiment is given. This framework provides a powerful tool for assessing the capabilities and limitations of performing quantum information processing tasks using current experimental techniques. The Gottesman-Knill theorem is generalized to the infinite-dimensional representations of the group stabilizer formalism and further generalized to include non-invertable semigroup transformations, providing a theorem for the efficient classical simulation of operations within this framework. As a result, we place powerful constraints on obtaining computational speedups using current techniques in quantum optics.