Good quantum error-correcting codes exist

A. R. Calderbank and Peter W. Shor
Phys. Rev. A 54, 1098 – Published 1 August 1996
PDFExport Citation

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=1-2H2(2t/n) where H2(p) is the binary entropy function -plog2p-(1-p)log2(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

Authors & Affiliations

A. R. Calderbank and Peter W. Shor

  • AT&T Research, 600 Mountain Avenue, Murray Hill, New Jersey 07974

References (Subscription Required)

Click to Expand
Issue

Vol. 54, Iss. 2 — August 1996

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×