Quantum Resource Theories

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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 non-equilibrium states-thermal, mechanical, chemical, etcetera-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 processing 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 states besides entanglement that are being studied as resources: for instance, the extent to which a state breaks symmetries, the extent to which a state 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 resource states? If one particular resource state cannot be converted to another deterministically, can it be done nondeterministically, 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 states that are reversibly interconvertible in the limit of asymptotically-many copies of the resource and to determine the rates of interconversion. ****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, etcetera---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.********