Quantum Cryptography in Noisy Channels

TL;DR

This paper proves the security of quantum cryptography in noisy channels, demonstrating equivalence of schemes, and shows that channel performance approaches noiseless limits as error rates decrease, with implications for efficiency improvements.

Contribution

It provides a complete security proof for quantum cryptography in noisy environments and establishes equivalence between polarization and EPR-based schemes.

Findings

Security holds against all eavesdropping including coherent attacks.

Performance approaches noiseless channel as error rate decreases.

Efficiency of quantum schemes can be doubled by basis probability adjustments.

Abstract

We provide a complete proof of the security of quantum cryptography against any eavesdropping attack including coherent measurements even in the presence of noise. Polarization-based cryptographic schemes are shown to be equivalent to EPR-based schemes. We also show that the performance of a noisy channel approaches that of a noiseless one as the error rate tends to zero. (i.e., the secrecy capacity $C_s (\epsilon) \to C_s (0)$ as $\epsilon \to 0$.) One implication of our results is that one can {\it double} the efficiency of a most well-known quantum cryptographic scheme proposed by Bennett and Brassard simply by assigning vastly different probabilities to the two conjugate bases.