1201.1256 (Victor Veitch et al.)

Negative Quasi-Probability Representation is a Necessary Resource for
Magic State Distillation    [PDF]

Victor Veitch, Christopher Ferrie, Joseph Emerson

The magic state model of quantum computation gives a recipe for universal
quantum computation using perfect Clifford operations and repeat preparations
of a noisy ancilla state. It is an open problem to determine which ancilla
states enable universal quantum computation in this model. Here we show that
for systems of odd dimension a necessary condition for a state to enable
universal quantum computation is that it have negative representation in a
particular quasi-probability representation which is a discrete analogue to the
Wigner function. This condition implies the existence of a large class of bound
states for magic state distillation: states which cannot be prepared using
Clifford operations but do not enable universal quantum computation. This
condition also enables an efficient experimental test for distillability.

View original: http://arxiv.org/abs/1201.1256