Depolarizing behavior of quantum channels in higher dimensions

TL;DR

This paper investigates the properties of quantum channels in high-dimensional spaces, revealing non-uniqueness in gate fidelity and showing convergence to depolarizing channels, with methods for estimating fidelity minima.

Contribution

It proves new properties of quantum gate fidelity, including non-uniqueness and convergence results, advancing understanding of quantum channel behavior in higher dimensions.

Findings

Existence of non-depolarizing channels with constant gate fidelity

Gate fidelity converges to that of a depolarizing channel asymptotically

Methods for estimating the minimum gate fidelity

Abstract

The paper analyzes the behavior of quantum channels, particularly in large dimensions, by proving various properties of the quantum gate fidelity. Many of these properties are of independent interest in the theory of distance measures on quantum operations. A non-uniqueness result for the gate fidelity is proven, a consequence of which is the existence of non-depolarizing channels that produce a constant gate fidelity on pure states. Asymptotically, the gate fidelity associated with any quantum channel is shown to converge to that of a depolarizing channel. Methods for estimating the minimum of the gate fidelity are also presented.