Effect of Decoherence in Ekert-Protocol

TL;DR

This paper investigates how different types of decoherence, specifically depolarizing and amplitude damping channels, affect the robustness of the Ekert91 quantum cryptographic protocol, showing it is more resilient to amplitude damping.

Contribution

The study introduces and compares the effects of depolarizing and amplitude damping decoherence channels on the Ekert91 protocol, highlighting its greater robustness to amplitude damping.

Findings

Depolarizing channel disentangles the quantum channel more easily.

Ekert protocol is more robust to generalized amplitude damping.

Bell inequality computations confirm robustness differences.

Abstract

We have examined the effect of the decoherence in the Ekert91 quantum cryptographic protocol. In order to explore this issue we have introduced two major decoherences, the depolarizing channel and the generalized amplitude damping, between the singlet source and one of the legitimate users. It is shown that the depolarizing channel disentangles the quantum channel more easily than the generalized amplitude damping. This fact indicates that the Ekert protocol is more robust to the generalized amplitude damping. We also have computed the Bell inequality to check the robustness or weakness of the Ekert91 protocol. Computation of the Bell inequality also confirms the robustness of the Ekert91 protocol to the generalized amplitude damping compared to the depolarizing channel.