Seminar 15. Quantum resource theories

Suppose we consider quantum theory and distinguish in it some subtheory of “simple” (free) transformations which is closed with respect to compositions and tensor products. For example, this could be a subtheory of non-entangling transformations or of Gaussian bosonic channels. By adding some resource (entanglement and nonlinearity, respectively) to this subtheory, one can perform arbitrary transformations. At the same time, free transformations cannot increase the resource. Thus, quantum mechanics can be viewed in terms of resource manipulation relative to the free sub-theory. Conversely, in order to study the properties of some resource, one can study the sub-theories to which it corresponds. Resources can be quantified by means of resource monotones – quantities that do not increase under free transformations. Often a monotone can be made operationally meaningful in various problems.