Chapter 12 provides an in-depth exploration of pure-state entanglement. It begins with a clear definition of quantum entanglement for pure states, emphasizing its critical role in quantum computing and communication. The chapter highlights various strategies for entanglement manipulation, encompassing deterministic, stochastic, and approximate methods. Quantification of bipartite entanglement is a key focus, with emphasis on entropy of entanglement and the Ky Fan norm-based entanglement monotones. Additionally, the chapter delves into entanglement catalysis and embezzlement of entanglement, presenting them as a nuanced nonintuitive phenomena that underscore the challenges of entanglement preservation during quantum operations. A notable aspect of this chapter is its connection between entanglement theory and the theory of majorization discussed in Chapter 4. Through a comprehensive treatment of these topics, the chapter equips readers with a robust understanding of the intricacies of pure-state entanglement theory.

Chapter 11 delves into the manipulation of quantum resources, the core aspect of quantum resource theories that explore the transformation and conversion of quantum states within a given resource theory framework. The chapter introduces the generalized asymptotic equipartition property and the generalized quantum Stein’s lemma, both foundational to understanding the asymptotic behavior of quantum resources. These concepts pave the way for discussing the uniqueness of the Umegaki relative entropy in quantifying the efficiency of resource conversion processes. Furthermore, the text explores asymptotic interconversions, detailing the conditions and limits for converting one resource into another when multiple copies of quantum states are considered. This analysis is pivotal for establishing the reversible exchange rates between different resources in the asymptotic limit. By providing a comprehensive overview of resource manipulation strategies, the chapter equips readers with the theoretical tools needed for advanced study and research in quantum resource theories, emphasizing both the single-shot and asymptotic domains.

Chapter 16, centered on the resource theory of nonuniformity, serves as an essential precursor to discussions on thermodynamics as a resource theory. It presents nonuniformity as a fundamental quantum resource, using it as a toy model to prepare for more complex thermodynamic concepts. In this model, free states are considered to be maximally mixed states, analogous to Gibbs states with a trivial Hamiltonian, providing a simplified context for exploring quantum thermodynamics. The chapter carefully outlines how nonuniformity is quantified, offering closed formulas for the conversion distance, nonuniformity cost, and distillable nonuniformity. These measures are explored both in the single-shot and the asymptotic domains. The availability of closed formulas makes this model particularly insightful, demonstrating clear, quantifiable relationships between various measures of nonuniformity.