Discrete Math Seminar: Vlad Gheorghiu

Abstract:

I will introduce the notion of stabilizer quantum error correcting codes and perfect quantum secret sharing schemes. Then I will illustrate how, using any given stabilizer code, one can always construct a perfect quantum secret sharing scheme out of it by allowing the sharing of extra classical bits between the dealer and the players.

Next I will describe a general scheme of reducing the amount of classical communication, then prove that the scheme is optimal for the stabilizer code being used.
The optimality proof is based on the fact that the correlations between the dealer and the players can be fully described by an "information" group, a subgroup of the symplectic Weil-Heisenberg group. The symplectic structure
of the information group effectively gives the minimum number of classical bits required. Finally I will provide an explicit protocol that achieves the bound by employing
the notion of "twirling" (or scrambling) the information group.

The talk will be self-contained and no prior exposure to quantum information is assumed. Most ideas will be illustrated by simple examples.