Optimal Implementation for the B92 Protocol

This project investigates the optimal implementation of the B92 quantum key distribution (QKD) protocol. The goal is to determine the optimal non-orthogonal angle that maximises the secure key generation rate under varying noise conditions. The model assumes that all noise (error rate) originates from eavesdropping attacks and is evaluated against collective and individual attack models.

A detailed dissertation paper describing the algorithms and discussion of results is available upon request.

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Main Takeaway

Key Results:

• Max secure key rate (R) for both attack types is approximately 0.50 at negligible noise (ε ≈ 0).
• Cutoff noise threshold (where R >= 0.1) is around ε ≈ 0.1 for both attack types.
• Across the noise range:
  • Individual attacks consistently maintain slightly higher ( R ) than collective attacks for the same ε.
  • Collective attacks degrade faster as noise increases.
• The comparative notebook (collective_vs_individual.ipynb) visually illustrates this performance gap among other analyses.

Limitations:
These results are based on an idealised model that assumes:

• All noise originates from eavesdropping.
• Perfect photon sources, detectors, and channel alignment.
• No optical imperfections, dark counts, or channel loss.

Because of these assumptions, the reported secure key rates and cutoff noise thresholds are overestimated compared to real-world B92 implementations.

Future Work:

• Incorporate realistic channel models with more parameters to be optimised.
• Extend analysis to other protocols (e.g., BB84) for benchmarking.

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How to Run

1. Run attack simulations

   • Execute b92_collective_attack.ipynb to simulate the collective attack scenario.
   • Execute b92_individual_attack.ipynb to simulate the individual attack scenario.
   • Results and plots are generated within each notebook.

2. Compare results

   • Run collective_vs_individual.ipynb to generate plots comparing collective and individual attack models.

3. Experimental notebook

   • b92_3states.ipynb is a work-in-progress and serves as a framework for exploring a 3-state B92 variant.

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Data Files

• collective_attack.csv and individual_attack.csv contain pre-generated results used by collective_vs_individual.ipynb for comparison.
• Running the simulation notebooks with different parameters will overwrite these files.

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Requirements

Install Python 3.8+, Jupyter Notebook, and the following dependencies:

pip install numpy scipy matplotlib pandas sympy jupyter