Quantum Theory

Professor R.B. Griffiths

Recent developments in atomic physics and quantum optics have made possible experimental studies of some of the unresolved issues in the foundations of quantum mechanics. The same techniques look promising for the construction of quantum computers and communication systems whose security is ensured by quantum cryptography. The quantum theory group at Carnegie Mellon is studying various problems related to quantum foundations and quantum information theory, including computation and cryptography.

The consistent histories approach to quantum theory was initiated at Carnegie Mellon in 1984, and was subsequently developed both here and at several other institutions. At the present time it provides the only fully consistent procedure for integrating probability theory into standard quantum mechanics without appealing to measurements or hidden variables. See the Consistent Histories Homepage for further information. It has been used to study a variety of problems in cosmology, quantum optics, and quantum information theory. Current research at Carnegie Mellon includes the application of consistent histories ideas to resolve some of the long-standing paradoxes of quantum theory, such as two-slit interference and Einstein-Podolsky-Rosen correlated states, without having to invoke mysterious long-range influences or other ghostly effects.

Significant Carnegie Mellon contributions to quantum information theory include: a major simplification in the final step of Shor's factorization algorithm, and a rigorous mathematical bound on the amount of information available to an eavesdropper in one of the better-studied schemes for quantum cryptography. Current research includes finding new ways to quantify the information contents of quantum systems, and algorithms for NMR quantum computing.

Recent Ph.D.s and Post-Graduation Positions

Chi-Sheng Niu (1998) "Quantum Copying and Simplification of the Quantum Fourier Transform" (Advisor: R. B. Griffiths); Mathematical finance