Lower bounds on the nonzero capacity of Pauli channels (original) (raw)
We study encodings that give the best known thresholds for the non-zero capacity of quantum channels, i.e., the upper bound for correctable noise, using an entropic approach to calculation of the threshold values. Our results show that Pauli noise is correctable up to the hashing bound. For a depolarizing channel, this approach allows one to achieve a non-zero capacity for a fidelity (probability of no error) of f = 0.80870. This paper complements [1], which investigated how a given quantum error correcting code can best correct a particular type of noise. That work made use of an entropic approach to calculation of thresholds of correctable noise, showing that an adaptive concatenation of the quantum code can improve the thresholds. In this paper, we apply the same entropic approach to finding the best known code for correcting a particular type of noise. We find codes that can correct all Pauli noise up to the hashing bound, i.e., the error rate per bit when the Shannon entropy of the noise S(N ) = 1, disproving the conjecture [3] that there exists some uncorrectable Pauli noise below the hashing bound.
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