#### Alladi Ramakrishnan Hall

#### Role of catalysts in quantum state transformation

#### Chandan Datta

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

*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 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 for general resource theories. For any quantum resource theory which contains resourcefree 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.

Done