Regularized maximal fidelity of the generalized Pauli channels

TL;DR

This paper investigates the asymptotic behavior of the maximal fidelity in generalized Pauli channels, deriving formulas for extremal fidelities, showing multiplicativity for many channels, and computing regularized fidelities for channels governed by time-local master equations.

Contribution

It provides new formulas for extremal fidelities, demonstrates multiplicativity in broad cases, and extends the analysis to channels described by time-local master equations.

Findings

Formulas for extremal channel fidelities

Multiplicativity of key quantities for many channels

Regularized maximal fidelity for channels with master equations

Abstract

We consider the asymptotic regularization of the maximal fidelity for the generalized Pauli channels, which is a problem similar to the classical channel capacity. In particular, we find the formulas for the extremal channel fidelities and the maximal output $\infty$-norm. For wide classes of channels, we show that these quantities are multiplicative. Finally, we find the regularized maximal fidelity for the channels satisfying the time-local master eqeuations.