Quantum holonomy in nonAbelian theories

Atushi Tanaka, Taksu Cheon

Taksu Cheon, Atushi Tanaka, Sanguk Kim

Daniel K. L. Oi

An incomplete quantum measurement can induce nontrivial dynamics between degenerate subspaces, a closed sequence of such projections produces a nonabelian holonomy. We show how to induce unitary evolution on an initial subspace from such finite discrete sequences and also construct a near deterministic repeat-until-success protocol. We also prove necessary and sufficient criteria on the auxiliary Hilbert space dimension required for inducing isometries between subspaces.

N. Read, Moore, G

It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Fractional statistics can be extended to nonabelian statistics and examples can be constructed from conformal field theory. The Pfaffian state is related to the 2D Ising model and possesses fractionally charged excitations which are predicted to obey nonabelian statistics.

Jerzy Dajka, M. Szopa

Gregory Greenwell