Quantifying Operations with an Application to Coherence

Understand

To describe certain facets of non-classicality, it is necessary to quantify properties of operations instead of states.

• This is the case if one wants to quantify how well an operation detects non-classicality, which is a necessary prerequisite for its use in quantum technologies.
• To do so rigorously, we build resource theories on the level of operations, exploiting the concept of resource destroying maps.
• We discuss the two basic ingredients of these resource theories, the free operations and the free super-operations, which are sequential and parallel concatenations with free operations.