Quantum Resource Theories: An overview and some recent results

Andrés F. Ducuara

Chandan Datta, Tulja Varun Kondra, Marek Miller +1 more

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 catalysis enhances our ability to convert quantum states into each other under physical constraints. The nature of the constraints depends on the problem under study and can arise, e.g. from energy preservation. This article reviews the most recent developments in quantum catalysis and gives a historical overview of this research direction. We focus on the catalysis of quantum entanglement and coherence, and also discuss this phenomenon in quantum thermodynamics and general quantum resource theories. We review applications of quantum catalysis and also discuss the recent efforts on universal catalysis, where the quantum state of the catalyst does not depend on the states to be transformed. Catalytic embezzling is also considered, a phenomenon that occurs if the catalyst’s state can change in the transition.

Martin Bodo Plenio

Coherence is the resource that allows quantum technologies to go beyond what is possible in the classical world. Due to its usefulness, coherence deserves to be quantified, just as we do for petrol, electricity, etc. Explaining how to do so in rigorously and how the resulting theory relates to experiments will be the subject of this lecture.

Fabio Costa, Giulia Rubino, Cyril Branciard +2 more

In recent years, operational approaches to quantum foundations have been developed as a means of understanding the core principles and distinctive features of quantum theory. Such approaches typically view physical processes as sequences of operations, with earlier operations serving as causes of later effects. However, a growing literature is emerging on the possibility of relaxing this assumption and allowing for quantum indefiniteness in the causal order. This development stems from a variety of motivations, both fundamental and applied, including exploring the role of causality in quantum theory, the interplay between quantum theory and general relativity, and higher-order quantum computing. A prominent offshoot of this development is the emergence of indefinite causal order as a feasible resource for quantum information processing. This review provides an overview of the current state of the art in the field, covering the methodology underlying indefinite quantum causality within the so-called "process matrix formalism", outlining key results and experimental implementations, and discussing recent advances.

Iman Marvian

Gilad Gour