How did the field of quantum information begin? To my mind, it was when
John Wheeler formed his little group of students and postdocs at the
University of Texas in the early 1980s. David Deutsch (first quantum
algorithms), Benjamin Schumacher (inventor of the qubit), William
Wootters (no-cloning theorem, later quantum teleportation), and Wojciech
Zurek (quantum decoherence) were all there. Even Richard Feynman (father
of quantum computation) visited once. It was because Wheeler had a
single-minded purpose. Of every student who walked into his office ---even
the first-year undergraduate--- Wheeler would implore: “Give an
information theoretic derivation of quantum theory!” He saw that as the
only way to get true understanding of “the quantum.”
In this talk, I will outline how Wheeler’s old hope is still bearing
fruit in the context of Quantum Bayesianism (or QBism). Particularly,
that context points naturally to a study of a mysterious structure in
Hilbert space called the Symmetric Information Complete (SIC) quantum
measurement. When these structures exist (and it seems they do for all
finite dimensions, though no one has proven it!) they give a very clean
way of writing the Born rule in purely probabilistic terms. This gives
the hope that all the mathematical structure of quantum theory might be
derivable from one very basic gedankenexperiment. It’s not the double-slit
experiment that Feynman argued for in his Feynman Lectures, but one
might still appeal to his intuition and hope, “In reality, [this new
scenario] contains the only mystery [of quantum mechanics].” |