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Discrete Wigner functions and quantum computational speedup

Ernesto F. Galvao
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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.

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Ernesto F. Galvao. 2005-04-05. Discrete Wigner functions and quantum computational speedup. https://doi.org/10.1103/physreva.71.042302

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