Abstract
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(2t/n) where (p) is the binary entropy function -pp-(1-p)(1-p). Upper bounds on this asymptotic rate are given. © 1996 The American Physical Society.
- Received 12 September 1995
DOI:https://doi.org/10.1103/PhysRevA.54.1098
©1996 American Physical Society