Christopher Fuchs - Perimeter Institute, IQC
Abstract
Imagine if one could automate discovery in quantum information theory, finding a procedure by which to open up any random article in the 50 years of IEEE Transactions on Information Theory and translate its old result into a new one holding in the quantum world instead. In the process, one could hope the procedure would reveal all the improvements and all the limitations quantum theory provides the venue. Unfortunately, no one is there yet!
However one can dream, and the first step to making it a reality is to develop a formalism that helps put quantum information into terms as close as possible to classical information. The differences between the theories would then be built in explicitly. In the best of worlds, such a formalism might even unlock the puzzles of quantum information in the way that Feynman’s path integral formalism unlocked the puzzles of quantum electrodynamics a half century ago.
In this talk, I will explain the rudiments of one such formalism for finite dimensional quantum theory, the key arena for quantum information and computing. It is based on a still conjectured notion, the so-called Symmetric Informationally Complete (SIC) quantum measurements. What is particularly surprising is how their existence would allow a rewriting of the quantum mechanical Born rule to be a simple formula purely in terms of probabilities, instead of as usual, a formula in terms of complex quantum states and operators. Unfortunately it has been an open mathematical problem for over 35 years as to whether the SICs do indeed always exist. Much progress has been made recently, however, and I will sketch a few recent developments.