Quantum codes do not fix isotropic errors

TL;DR

This paper proves that quantum error correcting codes cannot fix isotropic errors, showing that such errors remain uncorrected even with ideal correction circuits, leading to loss of quantum information.

Contribution

It establishes that quantum codes do not reduce isotropic error variance and that error detection results in complete information loss.

Findings

Quantum codes do not reduce isotropic error variance.

Error detection leads to uniform distribution and information loss.

Quantum correction circuits do not introduce additional errors.

Abstract

In this work we prove that quantum error correcting codes do not fix isotropic errors, even assuming that their correction circuits do not introduce new errors. We say that a quantum code does not fix a quantum computing error if its application does not reduce the variance of the error. We also prove for isotropic errors that, if the correction circuit of a quantum code detects an error, the corrected logical $m-$qubit has uniform distribution and as a result, it already loses all the computing information.