UM research extends the frontiers of convex analysis in Quantum journal

A new publication in the open access and high-impact Quantum Journal by Dr Roberto Salazar from the Department of Communications and Computer Engineering, Faculty of Information & Communication Technology (ICT) at the University of Malta, together with international collaborators, develops a new mathematical framework for studying quantum resources beyond the traditional limits of convex analysis.

Echoing the geometry of historical star fortresses, including those found in Malta, the work introduces star resource theories, where star-shaped geometric structures provide a natural way to quantify quantum resources. These structures generalise the convex sets commonly used in quantum information theory, allowing researchers to describe a broader range of physical phenomena.

Quantum resource theories are mathematical frameworks for identifying and quantifying useful features of quantum systems, such as entanglement, coherence, and quantum correlations. Most existing theories rely on convexity: the idea that mixing two objects that carry no resource should again produce an object with no resource. This assumption is powerful and mathematically convenient, but it can exclude important quantum phenomena whose natural structure is non-convex.

The paper, “Quantum Resource Theories beyond Convexity”, shows that star-shaped geometry can provide the right language for analyzing such cases. The framework includes standard convex theories as a special case, while also covering non-convex resources such as quantum discord, total correlations, and non-Markovian dynamics. The authors develop methods to quantify these resources, identify free operations, and demonstrate how they can improve performance in quantum discrimination tasks and in tests of quantum combs.

A key outcome of the work is the use of nonlinear witnesses, which can detect resources in cases where standard linear methods are not sufficient. The framework also connects to applications beyond quantum information, including mathematical questions related to unistochasticity, quantization of classical dynamics, and CP-symmetry violation in high-energy physics.

By extending resource theories beyond convexity, the publication opens new directions for the mathematical and operational analysis of quantum systems, while drawing inspiration from a geometric idea closely linked to Malta’s architectural heritage.