Environment-Assisted Error Correction of Single-Qubit Phase Damping

TL;DR

This paper demonstrates how environment-assisted error correction can invert phase-damping errors on a single qubit, extends the scheme to mixed environments, and uncovers cases where correction worsens the state fidelity.

Contribution

It explicitly implements environment-assisted error correction for phase damping and explores its extension to mixed environments, revealing unexpected outcomes.

Findings

Successful inversion of phase damping errors on a single qubit.

Extension of correction scheme to mixed-state environments.

Discovery of scenarios where correction reduces fidelity.

Abstract

Open quantum system dynamics of random unitary type may in principle be fully undone. Closely following the scheme of environment-assisted error correction proposed by Gregoratti and Werner [M. Gregoratti and R. F. Werner, J. Mod. Opt. 50(6), 915-933 (2003)], we explicitly carry out all steps needed to invert a phase-damping error on a single qubit. Furthermore, we extend the scheme to a mixed-state environment. Surprisingly, we find cases for which the uncorrected state is closer to the desired state than any of the corrected ones.