Good quantum error-correcting codes exist

Published

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Calderbank, AR; Shor, PW

Published Date

  • January 1, 1996

Published In

Volume / Issue

  • 54 / 2

Start / End Page

  • 1098 - 1105

Electronic International Standard Serial Number (EISSN)

  • 1094-1622

International Standard Serial Number (ISSN)

  • 1050-2947

Digital Object Identifier (DOI)

  • 10.1103/PhysRevA.54.1098

Citation Source

  • Scopus