Structured Codes Improve the Bennett-Brassard-84 Quantum Key Rate

Details Structured Codes Improve the Bennett-Brassard-84 Quantum Key Rate Structured Codes Improve the Bennett-Brassard-84 Quantum Key Rate

2006-07-03

arxiv.org/abs/quant-ph/0607018v2

Phys. Rev. Lett. 100, 170502 (2008)

Physics

Quantum Physics

Final version. Title changed

Scientific paper

10.1103/PhysRevLett.100.170502

A central goal in information theory and cryptography is finding simple characterizations of optimal communication rates subject to various restrictions and security requirements. Ideally, the optimal key rate for a quantum key distribution (QKD) protocol would be given by {\em single-letter formula} involving a simple optimization over a single use of an effective channel. We explore the possibility of such a formula for one of the simplest and most widely used QKD protocols--Bennett-Brassard-84 (BB84) with one way classical post-processing. We show that a conjectured single-letter key-rate formula is false, uncovering a deep ignorance about asymptotically good private codes and pointing towards unfortunate complications in the theory of QKD. These complications are not without benefit--with added complexity comes better key rates than previously thought possible. We improve the threshold for secure key generation from a bit error rate of 0.124 to 0.129.

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