Discrete Quantum Causal Dynamics

Prakash Panangaden
School of Computer Science
McGill University

Joint work with
Richard Blute 
Department of Mathematics
University of Ottawa

and

Ivan T. Ivanov
School of Computer Science
McGill University

We give a mathematical framework to describe the evolution of an open
quantum systems subjected to finitely many interactions with classical
apparatuses.  The systems in question may be composed of distinct, spatially
separated subsystems which evolve independently but may also interact. This
evolution, driven both by unitary operators and measurements, is coded in a
mathematical structure in such a way that the crucial properties of
causality, covariance and entanglement are faithfully represented.

In our work we also showed how our framework may be expressed using the
language of (poly)categories and functors.  Remarkably, important physical
consequences - such as covariance - follow directly from the functoriality
of our axioms.  We established links between the physical picture we
propose and linear logic.  Specifically we show that the refined logical
connectives of linear logic can be used to describe the entanglements of
subsystems in a way.  Furthermore, we show that there is a 
correspondence between the evolution of a given system and deductions in a
certain formal logical system based on the rules of linear logic.  We
conclude with some remarks about a possible language and type theory for
quantum computing.