Abstract: The error threshold of a one-parameter family of quantum channels is defined as the largest noise level such that the quantum capacity of the channel remains positive, which in turn guarantees existence of quantum error correction codes. Here, we study the error thresholds of channels arising from probabilistic Pauli errors. To this end, we determine lower bounds on the quantum capacity of these channels by evaluating the coherent information of so-called graph states affected by Pauli noise. Graph states are a subclass of stabilizer states and uniquely defined by a simple undirected graph. The main tools for our results are a) a simplified analysis of the channel action on graph states using the language of homomorphic group actions, and b) using strong generating systems for permutation groups to implement the algorithm in a computationally efficient manner. We provide an extensive analysis of known good codes such as repetition codes and cat codes in the whole Pauli channel simplex. Furthermore, we identify a novel family of quantum codes based on tree graphs with desirable error correction properties. This meeting will be a Zoom meeting! To participate, go to https://illinois.zoom.us/j/314999665 (please watch out for changes)
