Quantum Information Theory
Quantum mechanics can be viewed as a non-classical probability calculus, in which distinct random quantities generally can't be measured simultaneously to arbitrary accuracy. This limitation on simultaneous measurability allows the joint state of a pair of quantum systems to exhibit correlations that are stronger than is possible classically; such joint states, nowadays referred to as entangled states, are at the root of most of what has been thought mysterious about quantum mechanics, from Schrodinger's cat to the EPR "paradox."
Beginning in the early 1980s, it was realized that entangled states could be regarded as non-classical channels over which information can be transmitted between quantum systems—often in ways that are classically impossible. An entire field, Quantum Information Theory (QIT) has grown up around this observation, and is today a well-established, exciting, and very rapidly expanding area of mathematical physics, with important links to both pure mathematics and theoretical computer science. At the same time, the subject is largely accessible to undergraduate students with a strong grounding in linear algebra and some exposure to elementary classical probability theory. Among other things, this summer's REU at Susquehanna will focus on the possibility to extend results of quantum information theory to still more general probabilistic models.
