The quantum erasure channel (QEC) is considered. Codes for the QEC have to\ncorrect for erasures, i. e., arbitrary errors at known positions. We show that\nfour qubits are necessary and sufficient to encode one qubit and correct one\nerasure, in contrast to five qubits for unknown positions. Moreover, a family\nof quantum codes for the QEC, the quantum BCH codes, that can be efficiently\ndecoded is introduced.\n
A quantum error-correcting code is defined to be a unitary mapping (encoding)\nof k qubits (2-state quantum systems) into a subspace of the quantum state\nspace of n qubits such...
A group theoretic framework is introduced that simplifies the description of\nknown quantum error-correcting codes and greatly facilitates the construction\nof new examples. Cod...
I develop methods for analyzing quantum error-correcting codes, and use these\nmethods to construct an infinite class of codes saturating the quantum Hamming\nbound. These codes...
The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered. T...
I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channe...
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