Efficiently implementable codes for quantum key expansion

Abstract

The Shor-Preskill proof of the security of the BB84 quantum key distribution protocol relies on the theoretical existence of good classical error-correcting codes with the ``dual-containing'' property. A practical implementation of BB84 thus requires explicit and efficiently decodable constructions of such codes, which are not known. On the other hand, modern coding theory abounds with non-dual-containing codes with excellent performance and efficient decoding algorithms. We show that the dual-containing constraint can be lifted at a small price: instead of a key distribution protocol, an efficiently implementable key expansion protocol is obtained, capable of increasing the size of a pre-shared key by a constant factor.

4 pages, 1 figure. The new version has the title changed, the abstract, introduction and conclusion rewritten. To appear in PRA Rapid Communications

References in corpus (5)

• Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
• Good Quantum Error-Correcting Codes Exist
• Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long Distances
• Distillation of secret key and entanglement from quantum states
• Correcting Quantum Errors with Entanglement

Cited by in corpus (10)

• Catalytic quantum error correction
• Entanglement-Assisted Quantum Error-Correcting Codes with Imperfect Ebits
• Entanglement-Assisted Quantum Convolutional Coding
• Public and private communication with a quantum channel and a secret key
• Entanglement-assisted Coding Theory
• Stabilizer Entanglement Distillation and Efficient Fault-Tolerant Encoders
• Convolutional Entanglement Distillation
• Problems in application of LDPC codes to information reconciliation in quantum key distribution protocols
• Family of Finite Geometry Low-Density Parity-Check Codes for Quantum Key Expansion
• From Information Theory Puzzles in Deletion Channels to Deniability in Quantum Cryptography