Title: Role of catalysts in quantum state transformation

Speaker: Dr. Chandan Datta, Heinrich Heine University Düsseldorf, Germany

Zoom Link: https://zoom.us/j/92357345273?pwd=NXNlRittdWRVb2dPM25lclpaOHh3UT09

Abstract: In chemistry, a catalyst is a substance which enables a chemical reaction or increases its rate, while remaining unchanged in the process. Instead of chemical reactions, quantum catalysts enhance our ability to convert quantum states into each other 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. Here we discuss the role of catalysts in various 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 the presence of entangled catalysts. Furthermore, for transformations between bipartite pure states, we prove the existence of a universal catalyst, which can enable all possible transformations in this setup. Another key issue in resource theories 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 for general resource theories. For any quantum resource theory which contains resource-free pure states, we show that there does not exist a finite set of (continuous and faithful) resource monotones which completely determines all state transformations. Furthermore, we discuss how these limitations can be surpassed by using quantum catalysts.