Small quantum networks in the qudit stabilizer formalism

Understand

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.