Quantum resource theories (QRTs) offer a highly versatile and powerful framework for studying different phenomena in quantum physics. From quantum entanglement to quantum computation, resource theories can be used to quantify a desirable quantum effect, develop new protocols for its detection, and identify processes that optimize its use for a given application. Particularly, QRTs have revolutionized the way we think about familiar properties of physical systems such as entanglement, elevating them from being just interesting fundamental phenomena to being useful in performing practical tasks. The basic methodology of a general QRT involves partitioning all quantum states into two groups, one consisting of free states and the other consisting of resource states. Accompanying the set of free states is a collection of free quantum operations arising from natural restrictions placed on the physical system, restrictions that force the free operations to act invariantly on the set of free states. The QRT then studies what information processing tasks become possible using the restricted operations. Despite the large degree of freedom in how one defines the free states and free operations, unexpected similarities emerge among different QRTs in terms of resource measures and resource convertibility. As a result, objects that appear quite distinct on the surface, such as entanglement and quantum reference frames, appear to have great similarity on a deeper structural level. This article reviews the general framework of a quantum resource theory, focusing on common structural features, operational tasks, and resource measures. To illustrate these concepts, an overview is provided on some of the more commonly studied QRTs in the literature.

Considerable work has recently been directed toward developing resource theories of quantum coherence. In this Letter, we establish a criterion of physical consistency for any resource theory. This criterion requires that all free operations in a given resource theory be implementable by a unitary evolution and projective measurement that are both free operations in an extended resource theory. We show that all currently proposed basis-dependent theories of coherence fail to satisfy this criterion. We further characterize the physically consistent resource theory of coherence and find its operational power to be quite limited. After relaxing the condition of physical consistency, we introduce the class of dephasing-covariant incoherent operations as a natural generalization of the physically consistent operations. Necessary and sufficient conditions are derived for the convertibility of qubit states using dephasing-covariant operations, and we show that these conditions also hold for other well-known classes of incoherent operations.

A resource theory of quantum coherence attempts to characterize the quantum coherence that exists in a given quantum system. Many different approaches to a resource theory of coherence have recently been proposed, with their differences lying primarily in the identification of “free” or “incoherent” operations. In this article, we compare a number of these operational classes. In particular, the recently introduced class of dephasing-covariant operations is analyzed, and we characterize the Kraus operators of such maps. A number of coherence measures are introduced based on relative Rényi entropies, and we study incoherent state transformations under different operational classes. In particular, we show that the incoherent Schmidt rank can be increased arbitrarily large by certain noncoherence generating operations. The distinction between asymmetry-based versus basis-dependent notions of coherence theory is clarified, and we further develop the resource theory of $N$ asymmetry, where $N$ is the group of all diagonal incoherent unitaries.

Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely nonclassical phenomenon provides a necessary ingredient in many quantum information tasks such as violating a Bell inequality or nonlocally steering part of an entangled state. In this Letter, we characterize incompatibility in terms of programmable measurement devices and the general notion of quantum programmability. This refers to the temporal freedom a user has in issuing programs to a quantum device. For devices with a classical control and classical output, measurement incompatibility emerges as the essential quantum resource embodied in their functioning. Based on the processing of programmable measurement devices, we construct a quantum resource theory of incompatibility. A complete set of convertibility conditions for programmable devices is derived based on quantum state discrimination with postmeasurement information.

Interest in building dedicated quantum information science and engineering (QISE) education programs has greatly expanded in recent years. These programs are inherently convergent, complex, often resource intensive and likely require collaboration with a broad variety of stakeholders. In order to address this combination of challenges, we have captured ideas from many members in the community. This manuscript not only addresses policy makers and funding agencies (both public and private and from the regional to the international level) but also contains needs identified by industry leaders and discusses the difficulties inherent in creating an inclusive QISE curriculum. We report on the status of eighteen post-secondary education programs in QISE and provide guidance for building new programs. Lastly, we encourage the development of a comprehensive strategic plan for quantum education and workforce development as a means to make the most of the ongoing substantial investments being made in QISE.