Ternary Quantum Eraser Cryptography

TL;DR

This paper introduces a ternary quantum eraser cryptography protocol that enhances security by using three polarization states and randomized photon ordering, reducing eavesdropper success probability.

Contribution

It extends binary quantum eraser protocols to a ternary system with improved security mechanisms and comparable efficiency, addressing previous vulnerabilities.

Findings

Eavesdropper success probability is bounded at 54%.

The protocol achieves 0.30 bits per photon efficiency.

Enhanced security through reduced state distinguishability and complex photon ordering.

Abstract

Quantum key distribution protocols based on the quantum eraser phenomenon offer an operational advantage: automatic identification of matching and mismatching encoding choices through interference, eliminating basis reconciliation. However, binary quantum eraser implementations permit an eavesdropper to recover Alice's encoded bit with $85\%$ probability. To overcome this constraint, we introduce a ternary quantum eraser protocol employing three polarization states with $120^\circ$ angular separation, transmitted in three-photon groups with randomized temporal ordering. This extension achieves enhanced security through two complementary mechanisms. First, the reduced distinguishability of symmetrically-arranged quantum states limits single-photon discrimination. Second, the combinatorial complexity of unknown photon ordering constrains multi-photon eavesdropping strategies. Security analysis against individual eavesdropping attacks within the four-dimensional path-polarization Hilbert space establishes that an eavesdropper's maximum success probability is bounded at $54\%$, substantially below the binary discrimination bound. The protocol maintains a binary-equivalent efficiency of 0.30 bits per photon, comparable to established binary QKD protocols at the sifted-rate level, while preserving the operational simplicity inherent to quantum eraser cryptography.