Miniworkshop on Quantum Foils

Unentangled Bit Commitment and the CBH Theorem

aula dottorato - MARTEDì 18 DICEMBRE, ore 14.00
  MATTHEW LEIFER, Waterloo University, CA

Matt Leifer completed his Ph.D. at the University of Bristol in 2003 under the supervision of Prof. Noah Linden (Title: Entangled Quantum Dynamics). From 2004-2006 he was a postdoc at the Perimeter Institute for Theoretical Physics and after a brief stint at the University of Cambridge he began a second postdoc at the University of Waterloo in 2007. Research interests include: Foundations of Quantum Theory, Quantum Bayesianism, Algorithms for simulating many-body quantum systems and Entanglement theory.


After briefly reviewing the convex sets framework, I will show that an exponentially secure bit commitment protocol exists in any theory within the framework that does not permit entangled states [1]. Combined with our earlier results on broadcasting [2], this provides a complete generalization of the theorem proved by Clifton, Bub and Halvorson that was aimed at characterizing quantum theory in terms of information theoretic constraints [3]. Their theorem was proved in the context of C*-algebraic theories, but unfortunately in the more general context of convex sets, the same axioms do not imply anything particularly close to quantum theory. If time permits, I will discuss a conjecture about the set of theories that do not permit bit commitment.

[1] H. Barnum, O. Dahlsten, M. Leifer and B. Toner, Nonclassicality without entanglement enables bit commitment (2007), submitted to IEEE Information Theory Workshop 2008, arXiv version to appear soon.
[2] H. Barnum, J. Barrett, M. Leifer and A. Wilce, Generalized No-Broadcasting Theorem (2007), to appear in Phys. Rev. Lett., arXiv:0707.0620
[3] R. Clifton, J. Bub and H. Halvorson, Characterizing quantum theory in terms of information-theoretic constraints, Foundations of Physics 33, 1561-1591 (2003), arXiv:quant-ph/0211089v2