Michael Westmoreland grew up in America, attending sixteen different schools in Texas, Illinois and Missouri before graduating from high school. He did his undergraduate work at M.I.T. and Rice University, earning a B. A. in Mathematics and Economics from the latter. He received his Ph. D. from the University of Texas - Austin under the direction of David Saltman. He joined the Denison faculty in 1990. Professor Westmoreland enjoys teaching a variety of math courses, including Calculus, Real Analysis, Measure Theory, Probability, Introduction to Proofs, Linear Algebra and Differential Equations, Abstract Algebra, Topology and Graph Theory. He also enjoys watching cooking, reading, and teaching the occasional adult Sunday School class at his local Methodist church.
My research focuses on the foundations of quantum mechanics. As this physical theory is understood through its mathematical models (a fancy way of saying no one has an intuitive understanding of quantum mechanics), questions about foundational issues are well suited for attack by mathematical methods. Quite often the approach taken by my collaborators and me involves methods drawn from information theory. One our key results – the classical capacity of quantum channels – is a prime example of the application of such information theoretic methods. This result not only sets bounds for actual physical methods of communication it also provides a physical meaning to the mathematical construct know as “quantum entropy.”
Recently I have conducted recent research with students studying the entanglement structure of finite vector spaces; that is vector space over finite fields. Entanglement is the feature of quantum systems that provides ability for quantum systems to be teleported and for the increased power offered by quantum computing. Entanglement is also the feature of quantum mechanics that caused scientists such as Einstein, Podolsky and Rosen to doubt the ultimate validity of quantum mechanics. Einstein is famous for referring to the “spooky action at a distance” that entanglement leads too. But every prediction made by entanglement based models has so far stood the test of experiment. In finite fields, much of the abstract structure of quantum mechanics is simplified but may of the odd properties of quantum systems remain. These finite systems provide a handy “test bed” for conjectures about entanglement. My students have expanded our knowledge about entanglement in such simple systems. Students undertaking such research learn the fundamentals of quantum mechanics and finite field theory.
- With B. Schumacher, “Reverend Bayes takes the Unexpected Examination”, Math Horizons, (September, 2008).
- With B. Schumacher, “Isolation and information flow in quantum dynamics”, Foundations of Physics, (May, 2012).
- With B. Schumacher, “Modal Quantum Theory”, Foundations of Physics, (May, 2012).
- With B. Schumacher, “Possibility, probability, and entanglement: Non-contextuality in modal quantum mechanics”, Foundations of Probability and Physics – 6, American Institute of Physics; Melville, New York (2012).
- With B. Schumacher, Quantum Processes, Systems and Information, Cambridge University Press; Cambridge, U.K. (2011).
Selected student research projects:
- Entanglement in rational function fields of finite characteristic, Ruijun Ma, 2013.
- Multiparty entanglement in finite vector spaces, Yige Li, 2011 - 2012.
- Entanglement in Finite Vector spaces, R. J. Singh, 2009 – 2010.