Approximate quantum error correction

TL;DR

This paper demonstrates that when the loss of coherent information in a quantum channel is minimal, approximate quantum error correction becomes feasible, extending the conditions under which quantum information can be reliably preserved.

Contribution

It establishes a link between small coherent information loss and the possibility of approximate error correction in quantum channels.

Findings

Small loss of coherent information enables approximate error correction.

Perfect correction is only possible if the channel does not decrease coherent information.

The results extend the understanding of quantum error correction beyond perfect correction.

Abstract

The errors that arise in a quantum channel can be corrected perfectly if and only if the channel does not decrease the coherent information of the input state. We show that, if the loss of coherent information is small, then approximate error correction is possible.