E91 performance depends on entanglement quality and analyzer orientation

A theoretical and computational study of the E91 quantum key distribution protocol found that the phase and purity of entangled input states can strongly affect its performance, while the relative orientation of polarization analyzers can modulate those effects. The researchers derived analytical expressions for the minimum quantum bit error rate and the Bell parameter and validated them using quantum computational tools. The analysis focused on entangled photon pairs of the kind that may emerge from semiconductor quantum-dot sources.

Such sources are prominent candidates for providing the bright, highly entangled photon pairs required by entanglement-based quantum key distribution. However, the study notes that photon pairs emitted by many such sources are anomalous Bell states with non-ideal relative phase and purity, making their suitability for distributing cryptographic keys an important question. By examining changes in the input states through the derived expressions, the team assessed how physical imperfections propagate through the E91 protocol.

The results show that quantum transmission performance is highly sensitive to both the phase and purity of the entangled inputs. The relative directions of the polarization analyzers also matter: their orientation can modify the effect of these imperfections on the protocol’s observed behavior. This was a theoretical and computational analysis rather than an experimental deployment of a cryptographic network.

Its scope is the effect of input-state phase, state impurity and polarization-analyzer orientation on the E91 protocol. The findings offer insight for evaluating realistic entanglement sources and for understanding how source quality and measurement arrangement shape the performance of entanglement-based quantum key distribution.

Subject of Research: Effects of imperfect entangled photon states and measurement orientation on E91 quantum key distribution performance

Article Title: Impact of dephased entanglement, mixed input states and varying measurement orientations on the reliability of cryptographic keys generated via the quantum protocol E91

Article References: Hernández-Borda, A. F., Rojas-Sepúlveda, M. P., & Ramírez-Gómez, H. Y. (2026). Impact of dephased entanglement, mixed input states and varying measurement orientations on the reliability of cryptographic keys generated via the quantum protocol E91. PLOS One, 21(10), e0360669. https://doi.org/10.1371/journal.pone.0360669

Image Credits: AI Generated

DOI: 10.1371/journal.pone.0360669

Keywords: E91 protocol, quantum key distribution, entangled photons, quantum dots, Bell parameter, quantum bit error rate, measurement orientation, entanglement purity, quantum cryptography, Impact, dephased, entanglement