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Quantifying operations with an application to coherence

Banff International Research Station for Mathematical Innovation and Discovery

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. This leads to defining properties of functionals that are well suited to quantify the resources of operations. We introduce these concepts at the example of coherence. In particular, we present two measures quantifying the ability of an operation to detect, i.e. to use, coherence, one of them with an operational interpretation, and provide methods to evaluate them. We also present an application of these concepts to an experiment in quantum optics.

Mathematics; Quantum theory; Operator theory; Mathematical physics

video/mp4

Author affiliation: Ulm University

2020-01-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73341

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/