Logic, Physics and Quantum Information Theory.

There have been striking new connections between logic and category theory on the one hand and quantum computation and quantum information theory on the other. These ideas are in flux and there are diverse threads of activity. In this workshop we hope to bring together people who might not have met otherwise and explore connections between these different research programs.

Perhaps the earliest use of categories in the foundations of quantum mechanics is due to Prof. Chris Isham of Imperial College who explored the use of toposes in the consistent histories approach to quantum mechanics. In the early years of this century, Abramsky, Coecke and Selinger have devloped categorical foundations of quantum mechanics emphasizing the role of monoidal structure. Shortly before, Blute, Ivanov and Panangaden had looked at connections between linear logic and causal quantum evolution. In the last few years there has been significant new research developing at Imperial College, Oxford, Halifax and other places.

In the area of quantum information theory there has been a flood of recent results including new source coding theorems, capacity theorem and even -- very recently -- new insights into the black hole information paradox due to Hayden and Preskill. Keye Martin has developed an algebraic and domain theoretic approach which encompasses quantum information theory. This builds on earlier work of Martin and Coecke on domains of classical and quantum states.

There is considerable activity occurring in topological quantum computation. This has strong connections to category theory but there are tantalizing glimpses of connections with categorical quantum mechanics and also to the one-way model.

Finally, there is very interesting recent work of Sorkin on "anhomomorphic" logic which may solve some of the problems with paradoxes of quantum mechanics. It is our hope that some connections will be forged and perhaps new collaborations will be sparked off by this meeting. Not everyone could be accomodated in the limited space available, but we hope to have a broad cross section of people and some students as well.