A mathematical theory of resources

By Bob Coecke, Tobias Fritz, Robert W. Spekkens. Information and Computation, 2014

340 citations recorded by the source corpus.

Many fields of science investigate states and processes as resources. Chemistry, thermodynamics, Shannon's theory of communication channels, and the theory of quantum entanglement are prominent examples. Questions addressed by these theories include: Which resources can be converted into which others? At what rate can many copies of one resource be converted into many copies of another? Can a catalyst enable a conversion? How to quantify a resource? We propose a general mathematical definition of resource theory. We prove general theorems about how resource theories can be constructed from theories of processes with a subclass of processes that are freely implementable. These define the means by which costly states and processes can be interconverted. We outline how various existing resource theories fit into our framework, which is a first step in a project of identifying universal features and principles of resource theories. We develop a few general results concerning resource convertibility.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/d6c0f9008cb48d8cf79d5c29bc046bbb1a8de28a

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

The role of quantum information in thermodynamics—a topical review (2015, background): “comprehensive comparison between the principles behind these and more general resource theories is made in [128] and as examples of a more abstract treatment in [16].”
Robustness of asymmetry and coherence of quantum states (2016, background): “Once free states and free operations are defined, the main aim of a resource theory resides in the study of the manipulation of the resource by the (chosen) free operations [21, 23].”
Measures and applications of quantum correlations (2016, background): “To help with this task, one can view QCs as a resource within the framework of resource theories [10, 60, 61].”
Quantum resource theories (2018, background): “Moreover, recently it was recognized that a resource theory can be formulated as a symmetric monoidal category (Coecke et al., 2016; Fritz, 2015).”
Colloquium: quantum coherence as a resource (2016, background): “…such resource theories was in fact initially pursued with the quantitative theory of entanglement (Horodecki et al., 2009; Plenio and Virmani, 2007) but has since spread to encompass a wider range of operational settings (Coecke et al., 2016; del Rio et al., 2015; Horodecki and Oppenheim, 2013b).”