Discrete Wigner functions and quantum computational speedup
Quantum Physics
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.quant-ph/0405070,
title = {Discrete Wigner functions and quantum computational speedup},
author = {Ernesto F. Galvao},
journal= {arXiv preprint arXiv:quant-ph/0405070},
year = {2007}
}
Comments
7 pages, 2 figures, RevTeX. v2: clarified discussion on dynamics, added refs., published version