Math @ Duke

Publications [#236048] of Robert Calderbank
Papers Published
 Calderbank, AR; Shor, PW, Good quantum errorcorrecting codes exist,
Physical Review A  Atomic, Molecular, and Optical Physics, vol. 54 no. 2
(1996),
pp. 10981105
(last updated on 2017/12/16)
Abstract: A quantum errorcorrecting code is defined to be a unitary mapping (encoding) of k qubits (twostate quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum errorcorrecting codes are shown to exist with asymptotic rate k/n = 12H2(2t/n) where H2(P) is the binary entropy function plog2p(1 p)log2(l  p). Upper bounds on this asymptotic rate are given.


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