Good quantum error-correcting codes exist
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (two-state 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 error-correcting codes are shown to exist with asymptotic rate k/n=1-2[Formula Presented](2t/n) where [Formula Presented](p) is the binary entropy function -p[Formula Presented]p-(1-p)[Formula Presented](1-p). Upper bounds on this asymptotic rate are given. © 1996 The American Physical Society.
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