Considerable work has recently been directed toward developing resource theories of quantum coherence. In this talk I will review the general structure of such resource theories, and I will argue that all currently proposed basis-dependent approaches to quantum coherence fail to be physically consistent. That is, the “free” or “incoherent” operations defined within these frameworks ultimately require the consumption of quantum coherence to be physically implemented. Despite this lack of consistence, I will explain how many of the currently proposed classes of incoherent operations still may be of physical interest. In particular, I will describe how entanglement and coherence can be related to each other through the tasks of resource dilution and resource distillation using local incoherent operations and classical communication.

This talk will cover joint work with Alex Streltsov et. al (arXiv:1507.08171), Min-Hsiu Hsieh (arXiv:1509.07458), and Gilad Gour (TBP).