# High-dimensional quantum teleportation under noisy environments

## TL;DR

This paper analyzes high-dimensional quantum teleportation fidelity under various noise types, deriving general formulas and classifying behaviors, with implications for improving teleportation in noisy environments.

## Contribution

It provides a comprehensive analysis of noise effects on qudit teleportation, deriving general fidelity expressions for multiple noise scenarios in arbitrary dimensions.

## Key findings

- Classified noise effects into four behavioral categories.
- Derived general fidelity formulas for arbitrary dimension and noise types.
- Identified conditions where increasing noise can improve fidelity.

## Abstract

We study the protocol of qudit teleportation using quantum systems subjected to several kinds of noise for arbitrary dimensionality $d$. We consider four classes of noise: dit-flip, $d$-phase-flip, dit-phase-flip and depolarizing, each of them corresponding to a family of Weyl operators, introduced via Kraus formalism. We derive a general expression for the average fidelity of teleportation in arbitrary dimension $d$ for any combination of noise on the involved qudits. Under a different approach we derive the average fidelity of teleportation for a more general scenario involving the $d$-dimensional generalization of amplitude damping noise as well. We show that all possible scenarios may be classified in four different behaviours and discuss the cases in which it is possible to improve the fidelity by increasing the associated noise fractions. All our results are in agreement with previous analysis by Fortes and Rigolin for the case of qubits (Phys. Rev. A, 92 012338, 2015).