Prof Bob Coecke
Dr Terry Rudolph
Notions of complementarity in generalized process theories
Quantum foundations has a number of distinct goals, aiming to further our understanding of quantum theory or quantum-like theories of nature. One of these is the search for and analysis of non-classical or quantum effects. These may reveal important quantum-like or classical-like features which the world may or may not exhibit. Another important aim of quantum foundations is to provide an adequate interpretation and a thorough analysis of the axioms of quantum theory. Combining these, we can then determine fundamental principles from which the quantum formalism can be derived. This should eventually lead to a thorough conceptual and mathematical underpinning of quantum theory without any inconsistencies.
An alternative approach to foundations is to examine a larger space of hypothetical theories containing quantum theory. This allows us to formalize and clarify the different ways in which the world could possibly work and where quantum mechanics fits with respect to these possibilities. Such an analysis of mathematical theories of nature requires a high level of abstraction guided by deep and novel physical intuition.