Discrete Wigner functions and quantum computational speedup
Abstract
Description
In [Phys. Rev. A 70, 062101 (2004)] Gibbons et al. defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize a set C_d of states having non-negative W simultaneously in all definitions of W in this class. For d<6 I show C_d is the convex hull of stabilizer states. This supports the conjecture that negativity of W is necessary for exponential speedup in pure-state quantum computation.
7 pages, 2 figures, RevTeX. v2: clarified discussion on dynamics, added refs., published version
7 pages, 2 figures, RevTeX. v2: clarified discussion on dynamics, added refs., published version