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.