We study achievable secret key rates for the Bennett-Brassard-84 (BB84) quantum key distribution protocol with one way classical post-processing. Specifically, we characterize the performance of a family of error correcting codes when used in the information reconciliation phase of BB84. When combined with noisy processing, these codes allow secure key to be established for quantum bit error rates up to 0.129. This improvement over the previous best noise threshold of 0.124 illustrates, in contrast to the classical scenario, a marked advantage of structured codes over random codes when used for quantum key distribution. Our results are intimately connected to degenerate quantum codes, which we briefly discuss.
We study achievable secret key rates for the Bennett-Brassard-84 (BB84) quantum key distribution protocol with one way classical post-processing. Specifically, we characterize the performance of a family of error correcting codes when used in the information reconciliation phase of BB84. When combined with noisy processing, these codes allow secure key to be established for quantum bit error rates up to 0.129. This improvement over the previous best noise threshold of 0.124 illustrates, in contrast to the classical scenario, a marked advantage of structured codes over random codes when used for quantum key distribution. Our results are intimately connected to degenerate quantum codes, which we briefly discuss.
A quantum key distribution protocol(QKD), known as BB84, was developed in 1984 by Charles Bennett and Gilles Brassard. The protocol works in two phases which are quantum state transmission and conventional post processing. In the first phase of BB84, raw key elements are distributed between two legitimate users by sending encoded photons through quantum channel whilst in the second phase, a common secret-key is obtained from correlated raw key elements by exchanging messages through a public channel e.g.; network or internet. The secret-key so obtained is used for cryptography purpose. Reconciliation is a compulsory part of post processing and hence of quantum key distribution protocol. The performance of a reconciliation protocol depends on the generation rate of common secret-key, number of bits disclosed and the error probability in common secrete-key. These characteristics of a protocol can be achieved by using a less interactive reconciliation protocol which can handle a higher initial quantum bit error rate (QBER). In this paper, we use a simple Bose, Chaudhuri, Hocquenghem (BCH) error correction algorithm with simplified syndrome table to achieve an efficient reconciliation protocol which can handle a higher quantum bit error rate and outputs a common key with zero error probability. The proposed protocol efficient in removing errors such that it can remove all errors even if QBER is 60%. Assuming the post processing channel is an authenticated binary symmetric channel (BSC).
A central goal in information theory and cryptography is finding simple characterizations of optimal communication rates under various restrictions and security requirements. Ideally, the optimal key rate for a quantum key distribution (QKD) protocol would be given by a single-letter formula involving optimization over a single use of an effective channel. We explore the possibility of such a formula for the simplest and most widely used QKD protocol, Bennnett-Brassard-84 with one-way classical postprocessing. We show that a conjectured single-letter formula is false, uncovering a deep ignorance about good private codes and exposing unfortunate complications in the theory of QKD. These complications are not without benefit-with added complexity comes better key rates than previously thought possible. The threshold for secure key generation improves from a bit error rate of 0.124 to 0.129.
Abstract. We study the advantages to be gained in quantum key distribution (QKD) protocols by combining the techniques of local randomization, or noisy preprocessing, and structured (nonrandom) block codes. Extending the results of [Smith, Renes, and Smolin, quant-ph/0607018] pertaining to BB84, we improve the best-known lower bound on the error rate for the 6-state protocol from 14.11 % for local randomization alone to at least 14.59%. Additionally, we also study the effects of iterating the combined preprocessing scheme and find further improvements to the BB84 protocol already at small block lengths. PACS numbers: 03.67.Dd Quantum cryptography and communication security 03.67.Hk Quantum communicationImproved one-way rates for BB84 and 6-state protocols 2 1.
This paper demonstrates ways to improve the post-processing phase of BB84-based Quantum Key Distribution (QKD) while maintaining Information-Theoretic security. Maximum entropy in the distilled bits can be achieved provided that we follow certain rules on which bits are sacrificed based on the properties of the generator matrix. We use standard decoder techniques to distill bits and establish Information-Theoretic security and provide insights into how those techniques can be adapted to provide greater bit throughput. Finally, we compare popular coding schemes in BB84 post-processing as a basis for code selection and discover at low initial Bit Error Rates (BER), a Polar 4/5 or Hamming* give the best performance and for higher initial BER, the LDPC 3/4 and Hamming* (a modified Hamming code) give the best performance [1] [2] [9] [10].
In data post-processing for quantum key distribution, it is essential to have a highly efficient error reconciliation protocol. Based on the key redistribution scheme, we analyze a one-way error reconciliation protocol by data simulation. The relationship between the error correction capability and the key generation efficiency of three kinds of Hamming code are demonstrated. The simulation results indicate that when the initial error rates are(0,1.5%],(1.5,4%], and(4,11%], using the Hamming(31,26),(15,11), and(7,4) codes to correct the error, respectively, the key generation rate will be maximized. Based on this, we propose a modified one-way error reconciliation protocol which employs a mixed Hamming code concatenation scheme. The error correction capability and key generation rate are verified through data simulation. Using the parameters of the posterior distribution based on the tested data, a simple method for estimating the bit error rate(BER) with a given confidence interval is estimated. The simulation results show that when the initial bit error rate is 10.00%, after 7 rounds of error correction, the error bits are eliminated completely, and the key generation rate is 10.36%; the BER expectation is 2.96×10-10, and when the confidence is 95% the corresponding BER upper limit is 2.17×10-9. By comparison, for the single(7,4) Hamming code error reconciliation scheme at a confidence of 95%,the key generation rate is only 6.09%, while the BER expectation is 5.92×10-9, with a BER upper limit of 4.34×10-8. Hence, our improved protocol is much better than the original one.
In data post-processing for quantum key distribution, it is essential to have a highly efficient error reconciliation protocol. Based on the key redistribution scheme, we analyze a one-way error reconciliation protocol by data simulation. The relationship between the error correction capability and the key generation efficiency of three kinds of Hamming code are demonstrated. The simulation results indicate that when the initial error rates are(0,1.5%],(1.5,4%], and(4,11%], using the Hamming(31,26),(15,11), and(7,4) codes to correct the error, respectively, the key generation rate will be maximized. Based on this, we propose a modified one-way error reconciliation protocol which employs a mixed Hamming code concatenation scheme. The error correction capability and key generation rate are verified through data simulation. Using the parameters of the posterior distribution based on the tested data, a simple method for estimating the bit error rate(BER) with a given confidence interval is estimated. The simulation results show that when the initial bit error rate is 10.00%, after 7 rounds of error correction, the error bits are eliminated completely, and the key generation rate is 10.36%; the BER expectation is 2.96×10-10, and when the confidence is 95% the corresponding BER upper limit is 2.17×10-9. By comparison, for the single(7,4) Hamming code error reconciliation scheme at a confidence of 95%,the key generation rate is only 6.09%, while the BER expectation is 5.92×10-9, with a BER upper limit of 4.34×10-8. Hence, our improved protocol is much better than the original one.