Ternary Quantum Eraser Cryptography

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.