Elements of information theory
Elements of information theory
Quantum computation and quantum information
Quantum computation and quantum information
Graphs and Hypergraphs
Generatingfunctionology
Analytic Combinatorics
On Cayley Graphs, Surface Codes, and the Limits of Homological Coding for Quantum Error Correction
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
Quantum LDPC codes with positive rate and minimum distance proportional to n 1/2
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Modern Coding Theory
Quantum error correction via codes over GF(4)
IEEE Transactions on Information Theory
Upper bounds on the rate of LDPC codes
IEEE Transactions on Information Theory
Sparse-graph codes for quantum error correction
IEEE Transactions on Information Theory
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Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, R ≤ 1 - 2p, for stabilizer codes: we also derive an improved upper bound of the form R ≤ 1-2p-D(p) with a function D(p) that stays positive for 0 p We obtain an application to percolation theory for a family of self-dual tilings of the hyperbolic plane. We associate a family of low density stabilizer codes with appropriate finite quotients of these tilings. We then relate the probability of percolation to the probability of a decoding error for these codes on the quantum erasure channel. The application of our upper bound on achievable rates of low density stabilizer codes gives rise to an upper bound on the critical probability for these tilings.