Quantum-inspired mathematics

Set theory can be used as a foundational framework for mathematics. But sets are intended to be considered as collections of objects. These are supposed to be distinguishable and to have well defined properties. Intuitively speaking, the collection of natural numbers, or the planets of the solar system, can be considered as sets. In this way, set theory is inspired by the properties of classical objects, which can be distinguished counted, and have well defined properties independently of the context in which they are considered. But quantum physics has showed us objects of a different kind. Remarkably, quantum systems can be prepared in states in which they are indistintinguishable by any operational means. The peculiar properties of quantum systems have inspired non-standard mathematical frameworks that intend to describe collections of quantum objects. Examples of these frameworks are QuasiSet theory, Quasets, and Quantum Mereologies.

a group of black balls sitting on top of a white surface

Our research

We have extensively worked in the development of QusiSet theory, trying to find direct applications to quantum physics. It is remarkable that this framework can be used to formulate quantum mechanics in the Fock-space. We have also worked with Quaset theory, trying to describe quantum systems with undefined properties. The development of non-standard frameworks is also relevant for building a quantum mereology, that is, a theory of the relationship between wholes and parts for quantum objects.

Our goals

There are several reasons for developing non-standard mathematical frameworks and mereologies. First, to study a mathematics inspired by quantum physis is interesting on its own for the philosophy of logic and mathematics. Second, by incorporating a logical framework based in the properties of quantum systems, one obtains a way of describing quantum physics that avoids the so called surplus structure problem. Finally, the existence of a formal language for describing quantum systems allows for a non-ambiguous logical description of the intuitive concepts used by quantum physicists.

Our team

Our strength lies in our individuality. Set up by Esther Bryce, the team strives to bring in the best talent in various fields, from architecture to interior design and sales.