  It is known that if the quantum gates in a proposed quantum computer are so
noisy that they are incapable of generating entanglement, then the device can
be efficiently simulated classically. If the measurements and single particle
operations are restricted, then the same statement can be true for generalised
non-quantum notions of entanglement. Here we show that this can improve the
applicability of limited-entanglement simulation algorithms. In particular, we
show that by using a non-quantum notion of separability a classical simulation
algorithm of Harrow & Nielsen can efficiently simulate magic state quantum
computers with noisy CNOTs (but otherwise ideal) for joint depolarising
strengths of 272/489 ~ 56%, in comparison to noise levels of 2/3 ~ 66% required
if the algorithm uses quantum notions of separability. This suggests that
quantum entanglement may not be the most appropriate notion of entanglement to
use when discussing the power of stabilizer based quantum computers.

Quantum Physics