Alladi Ramakrishnan Hall

Catalysis in quantum resource theories

Chandan Datta

Institute for Theoretical Physics III, Heinrich Heine University Düsseldorf, Germany

Quantum resource theories introduced in quantum information science provide a mathematically rigorous way to study various resources, for example, entanglement. One of the important questions in any resource theory is to study state transformations under some physical constraints. The nature of the constraints depends on the problem under study; for instance, in entanglement theory, the parties are spatially separated, and we can perform only local operations on them. Notably, there exist state transformations that cannot be realised under some specified operations. In contrast, those impossible transformations can sometimes be realised with the help of an auxiliary system, known as a catalyst, that remains unchanged in the process. Here we discuss the role of catalysts in various quantum resource theories. One of the important questions in the resource theory of entanglement is to study entangled state transformations under local operations and classical communications. We investigate different aspects of entanglement catalysis for quantum state transformations. We prove that entanglement entropy completely characterises bipartite pure state transformations in weakly approximate correlated catalysis. We further discuss the structure of the catalyst and the protocol to realise a given transformation. Furthermore, for transformations between bipartite pure states, we prove the existence of a universal catalyst, which can enable all possible transformations in this setup. We also discuss the structure of the universal catalyst. As an application, we discuss the role of catalysts in entanglement distribution via noisy channels. Another key issue in resource theory is resource quantification. In fact, resource quantification and state transformation are closely related, and in order to identify state transformations, we typically look for a set of criteria based on resource monotones (resource quantifiers). Here we explore their connection to general resource theories. For any quantum resource theory that contains resource-free pure states, we show that there does not exist a finite set of (continuous and faithful) resource monotones that completely determines all state transformations. Furthermore, we discuss how these limitations can be surpassed by using quantum catalysts.