In the first part of the talk I will present extensions of quantum hypothesis testing to the case of non-indenpendent and identically distributed states; I will consider the setting where one would like to discriminate many copies of a given quantum state from a family of non-i.i.d. states. We say such a family of states has the exponential distinguishability (ED) property if the discrimination can be performed with exponential acuracy, in the number of copies of the first state. I will present certain conditions on sets of states under which we can prove the ED property. The proof combines recent developments on the characterization of permutation-symmetric quantum states, such as the exponential de Finetti theorem, and concepts from entanglement theory, such as the idea of non-lockability in entanglement measures.

In the second part of the talk, I will consider a new approach to the study of resource theories. These theories analyse the implications of restrictions on the physical processes available to the convertability of a physical state into another. A well-known example of a resource theory is entanglement theory, which emerges when distant parties only have access to local operations and classical communication. I will argue that whenever the set of non-resource states satisfies the ED property, then one can achieve reversible trasformations of the resource states in the framework where all operations not capable of generating resource can be used. Moreover, I will show that the unique measure fully charaterizing the rates of convertability is given by the optimal rate of distinguishability of a resource state to non-resource states. I will end up showing two applications of this result to entanglement theory.