Reply to Fahmi and Golshani's comment on "Quantum key distribution in the Holevo limit"

TL;DR

This paper addresses and corrects a quantum key distribution protocol to accurately demonstrate achieving the Holevo limit, clarifying previous inaccuracies and providing an improved protocol.

Contribution

It corrects a prior quantum key distribution protocol to properly achieve the Holevo limit, enhancing understanding of quantum communication efficiency.

Findings

The original protocol did not achieve efficiency one as claimed.

The corrected protocol accurately reaches the Holevo limit.

Clarifies the conditions for optimal quantum key distribution efficiency.

Abstract

As Fahmi and Golshani correctly point out, a protocol introduced in A. Cabello, Phys. Rev. Lett. 85, 5635 (2000), to show that a quantum key distribution protocol can have efficiency one (i.e., can achieve the Holevo limit), does indeed not have efficiency one. The corrected protocol, introduced in A. Cabello, Recent. Res. Devel. Physics 2, 249 (2001), is reproduced here.