What is the shape of Hilbert space? More precisely, what is the geometry of the set of quantum states? What symmetries does this sethave? This question is of deep importance to quantum information theory, and it is of deep importance to a surging school of thought in quantum foundations, the quantum Bayesian approach. This is a workshop organized with the hope of making significant progress with regard to a seemingly simple, but extremely recalcitrant, version of the question: the question of the existence of minimal symmetric informationally-complete (SIC) sets of pure quantum states.
The question is simply this: take the set of pure quantum states for a d-level system; these operators span the d^2 dimensional space of Hermitian operators. Can one create a regular simplex of d^2 vertices with elements drawn from this set? This is an almost trivial question--one of the most basic questions one can ask of a convex set--but it has a long unsolved history, ranging back, in one guise or another, at least 35 years.
The idea of the meeting is to gather the best people in quantum information theory who have given this problem significant thought, put them all in one place, and see progress made by any means! We'll start off with a fiery rendition of Henry V's St. Crispin's day speech:
This day is call'd the feast of Crispian.
He that outlives this day, and comes safe home,
Will stand a tip-toe when this day is nam'd,
And rouse him at the name of Crispian.
He that shall live this day, and see old age,
Will yearly on the vigil feast his neighbours,
And say 'To-morrow is Saint Crispian.'
Then will he strip his sleeve and show his scars,
And say 'These wounds I had on Crispian's day.'
Old men forget; yet all shall be forgot,
But he'll remember, with advantages,
What feats he did that day.
Roll up our sleeves, brace for the scars, and get to work. Each day will consist of morning talks, each on some aspect of the problem, with the afternoons reserved for round-table/chalkboard working sessions. The simple idea is to run the troops into the breach opened by these last years of research and finally defeat this SICkening problem!