Analysis of Noisy Environments on D‐Dimensional Quantum Secret Sharing

Abstract

Quantum secret sharing is a fundamental protocol for securely transmitting quantum as well as classical information. However, in practical quantum communication scenarios, the transmission of quantum information is inevitably influenced by environmental noise. Therefore, in this work, we analyze the robustness of multi‐dimensional quantum secret sharing schemes under four different noise models, namely amplitude damping (ad), depolarizing (d), dit flip (df), and phase flip (dpf). Each model captures a distinct type of quantum disturbance, providing insights into how different noise models affect the fidelity of secret reconstruction. In addition to state‐specific fidelity, we also evaluate the average fidelity over arbitrary pure qutrit secret states using the Haar, equivalently Fubini–Study, measure. This provides a state‐independent robustness indicator and allows a more meaningful comparison of the considered quantum secret sharing schemes when the dealer's secret state is arbitrary. Moreover, we observe that protocols involving a larger number of qudits generally exhibit higher implementation complexity and increased sensitivity to noise. Consequently, the fidelity degrades more rapidly. Moreover, it is observed that the amplitude damping noise shows the highest fidelity across most parameter ranges, suggesting a better preservation of quantum secret.