Abstract: Since the paper of Renes et al. [J. Math. Phys. 45, 2171 (2004)],
there has been much effort in the quantum information community to prove (or
disprove) the existence of symmetric informationally complete (SIC) sets of
quantum states in arbitrary finite dimension. In this talk, I will attempt
to strengthen the urgency of this question by showing that if SIC-sets
exist, they have some very nice properties.  Among these are 1) by a natural
measure of orthonormality, SIC-sets are as close to being an orthonormal
basis for the space of density operators as possible, and 2) in prime
dimensions, the standard construction for complete sets of mutually unbiased
bases and Weyl-Heisenberg covariant SIC-sets are intimately related: The
latter represent minimum uncertainty states for the former in the sense of
Wootters and Sussman.  Finally, I will discuss what quantum state space
looks like when expressed in SIC language.

Brief Biography of Professor Fuchs:

Research Interests:

Quantum information theory
Quantum communication and cryptography
Quantum foundations in the light of quantum information
Quantum control and quantum computation

Present Employment:
Member of Technical Staff, Bell Labs, Alcatel-Lucent

Education:
Ph. D. in Physics, May 1996, The University of New Mexico, Albuquerque, New
Mexico
Dissertation: "Distinguishability and Accessible Information in Quantum
Theory"
Advisor: Carlton M. Caves
B. S. in Physics, with High Honors, December 1987
B. S. in Mathematics, with High Honors, December 1987
The University of Texas at Austin, Austin, Texas

Honors, Professional Awards, and Invited Community Service:
Associate Editor, Quantum Information and Computation, Rinton Press, since
2000.
2-Year Member-at-Large, Executive Committee, American Physical Society
Topical Group on Quantum Information, 2007–2008.
Adjunct Professor of Physics and Astronomy, University of New Mexico,
Albuquerque, New Mexico, since 2006. (Adjunct Assistant Professor,
2000–2005.)
Member, Technology Experts Panel, United States Advanced Research and
Development Activity (ARDA) Roadmap for Quantum Cryptography, since 2003.
Member, National Science Foundation Review Panel on Mathematical Physics,
2005.
E. T. S. Walton Visitor Award, Science Foundation Ireland, consisting of the
compensation of my Bell Labs salary + 20% cash award + research funds for a
sabbatical to Communications Network Research Institute, Dublin, Ireland,
April 2003 – August 2004.
Guest Professor, Research Center for Quantum Communication, Tamagawa
University, Tokyo, Japan, since 2000.
Paper A27 below listed among the "top ten breakthroughs of the year 1998" by
the editors of Science.
Known citations in the ISI Science Citation Index > 2,000.

Professional Affiliations:
American Mathematical Society (member)
American Physical Society (member)
Center for Discrete Mathematics & Theoretical Computer Science (permanent
member)
Institute for Science and Interdisciplinary Studies (member)
International Quantum Structures Association (member)
Philosophy of Science Association (member)
William James Society (member)

Journals Refereed:
American Journal of Physics
Annals of Physics
European Physical Journal D
Europhysics Letters
Foundations of Physics
IEEE Transactions on Information Theory
International Journal of Quantum Information
Journal of Applied Mathematics
Journal of Mathematical Physics
Journal of Modern Optics
Journal of Optics
Journal of Physics A
Nature
Open Systems & Information Dynamics
Physica Scripta
Physical Reviews A & E
Physical Review Letters
Physics Letters A
Physics Today
Quantum Information and Computation
Quantum Information Processing
Studies in History and Philosophy of Modern Physics