  How much noise can a given quantum state tolerate without losing its
entanglement? For qudits of arbitrary dimension, I investigate this question
for two noise models: Global white noise, where a depolarizing channel is
applied to all qudits simultaneously, and local white noise, where a single
qudit depolarizing channel is applied to every qudit individually. Using a
unitary generalization of the Pauli group, I derive noise thresholds for
stabilizer states, with an emphasis on graph states, and compare different
entanglement criteria. The PPT and reduction criteria generally provide high
noise thresholds, however, it is difficult to apply them in the case of local
white noise. Entanglement criteria based on so-called sector lengths, on the
other hand, provide coarse noise thresholds for both noise models. The only
thing one has to know about a state to compute this threshold is the number of
its full-weight stabilizers. In the special case of qubit graph states, I
relate this question to a graph-theoretical puzzle and solve it for four
important families of states. For Greenberger-Horne-Zeilinger states under
local white noise, I obtain for the first time a noise threshold below which
so-called semiseparability is ruled out.
