Gauge invariant information concerning quantum channels

TL;DR

This paper investigates gauge-invariant properties of quantum channels, using the spectrum of superoperators to derive conditions for complete positivity and to express metrics like average gate fidelity, aiding in quantum process characterization.

Contribution

It introduces a gauge-invariant framework based on superoperator spectra for analyzing quantum channels, providing new necessary conditions and metric expressions.

Findings

Derived necessary conditions for complete positivity of qubit channels.

Expressed average gate fidelity using gauge-invariant spectral properties.

Highlighted the importance of spectrum-based invariants in quantum channel analysis.

Abstract

Motivated by the gate set tomography we study quantum channels from the perspective of information which is invariant with respect to the gauge realized through similarity of matrices representing channel superoperators. We thus use the complex spectrum of the superoperator to provide necessary conditions relevant for complete positivity of qubit channels and to express various metrics such as average gate fidelity.