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

Abstract

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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References in corpus (3)

• Distillation of secret key and entanglement from quantum states
• Degenerate Quantum Codes for Pauli Channels
• Noisy Preprocessing and the Distillation of Private States

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• A Survey on Quantum Channel Capacities
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• Dephrasure channel and superadditivity of coherent information
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• The Physics of Quantum Information: Complementarity, Uncertainty, and Entanglement
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• Experimental observation of coherent-information superadditivity in a dephrasure channel
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