Publications [#236048] of Robert Calderbank

Journal articles or Book chapters PUBLISHED

1. Calderbank, AR; Shor, PW, Good quantum error-correcting codes exist, Physical Review A Atomic Molecular and Optical Physics, vol. 54 no. 2 (January, 1996), pp. 1098-1105, American Physical Society (APS) [doi]
   (last updated on 2026/01/17)

   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[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.