Theories of dynamical quantum resources

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For any given kind of resource, one needs a theory to answer basic questions such as: which collections of resources can be converted into which others, and what are the ways in which a given conversion can be accomplished? Chemistry fits this mold, as it answers the question of how collections of chemicals available in abundance can be converted to other, more useful, products. Thermodynamics is another example, as it answers questions about how various sorts of nonequilibrium states-thermal, mechanical, chemical, etc-can be converted into others, for instance, how useful work can be extracted from a pair of heat baths at different temperatures. The poster child for the resource-theoretic approach today is entanglement theory. Although the notion of entanglement was introduced in the 1930s, it was not until the mid-nineties that we began to have a proper understanding of entanglement, after it was recognized to be useful for certain quantum information protocols. In other words, the turning point occurred when researchers began to study entanglement as a resource. Since then, entanglement theory has found applications not only in quantum computation, cryptography and communication, but in many other areas of physics, including the study of phase transitions, characterizing the ground states of many-body systems, holography in quantum field theories, and the black hole information-loss paradox. Inspired by this success, there are now many other properties of quantum systems, besides entanglement that are being studied as resources: for instance, the extent to which a quantum channel breaks symmetries, the extent to which a system deviates from thermal equilibrium, and the extent to which a quantum state is contextual. In addition to the basic questions above, this proposal aims to provide answers to questions such as: How does one measure the quality of different dynamical resources? If one particular resource channel cannot be converted to another deterministically, can it be done non-deterministically, and if so with what probability? What if one has access to a catalyst? A particularly fundamental problem is to identify the equivalence classes of quantum channels that can be used to simulate each other in the limit of asymptotically-many copies of the resource and to determine the rates of inter-conversion. Answering these concrete questions typically leads to significant new insights into the nature of the physical or information-theoretic phenomenon in question--entanglement, asymmetry, athermality, etc-- and provides a framework to organize theoretical results concerning those phenomena. As entanglement theory has demonstrated, the resource-theoretic approach has the capacity to revolutionize the way we think about familiar topics. Particularly, this research program will develop new methods in quantum information, improve our understanding of quantum physics in general, and help Canada establish its leadership in quantum science.