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Improved one-way rates for BB84 and 6-state protocols

O. Kern, Joseph M. Renes

Published Nov 27, 2012• 8 citations
OpenAlex

Abstract

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.

Related papers

Improved one-way rates for BB84 and 6-state protocols

O. Kern, Joseph M. Renes

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, {\em Physical Review Letters}, 100:170502] 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.

arXiv:0712.1494•Quantum Information and Computation•Sep 1, 2008•6 citations

Better codes for BB84 with one-way post-processing

Smith, G, Joseph M. Renes, John A. Smolin

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.

•Jul 3, 2006•3 citations

Tight asymptotic key rate for the Bennett-Brassard 1984 protocol with local randomization and device imprecisions

Erik Woodhead

Local randomization is a preprocessing procedure in which one of the legitimate parties of a quantum key distribution (QKD) scheme adds noise to their version of the key and was found by Kraus et al. [Phys. Rev. Lett. 95, 080501 (2005)] to improve the security of certain QKD protocols. In this article, the improvement yielded by local randomization is derived for an imperfect implementation of the Bennett-Brassard 1984 (BB84) QKD protocol, in which the source emits four given but arbitrary pure states and the detector performs arbitrarily aligned measurements. Specifically, this is achieved by modifying an approach to analyzing the security of imperfect variants of the BB84 protocol against collective attacks, introduced in [Phys. Rev. A 88, 012331 (2013)], to include the additional preprocessing step. The previously known improvement to the threshold channel noise, from 11% to 12.41%, is recovered in the special case of an ideal BB84 implementation and becomes more pronounced in the case of a nonideal source. Finally, the bound derived for the asymptotic key rate, both with and without local randomization, is shown to be tight with the particular source characterization used. This is demonstrated by the explicit construction of a family of source states and optimal attacks for which the key-rate bound is attained with equality.

arXiv:1405.5625•Physical Review A•Aug 6, 2014•9 citations

En-BB84: Advancements in Secure Quantum Key Distribution with Improved Error Resilience and Built-in Authentication

Yashwanth Venkat, D Preetha Evangeline, P Anandha Kumar

Quantum key distribution (QKD) is a method that enables secure communication between two parties by applying the ideas of quantum physics. By minimizing information leakage that can happen during the key generation process, privacy amplification is a technique used to improve the security of QKD. The technique involves processing the raw key obtained from QKD through a randomization procedure to remove any residual information that may have been leaked during the quantum transmission. While privacy amplification can significantly improve the security of QKD, the effectiveness of the technique is limited by the quality of the initial raw key. The BB84 QKD protocol has been improved with the proposed En-BB84 protocol, which includes built-in authentication and integrity checks. The En-BB84 protocol ensures secure distribution of secret keys and protects against tampering by attackers. Key distillation and error correction techniques are employed to extract a shorter, more secure shared secret key and correct errors introduced during qubit transmission. The protocol utilizes a four-state QKD approach, expanding on the traditional two-state scheme of BB84. A simulation of the En-BB84 protocol is demonstrated using a quantum circuit implemented with Qiskit in Python. The circuit employs various gates and operations, including Hadamard, CX, controlled swap, and RZ gates, to achieve encoding and error correction. Furthermore, we have designed a better protocol with improved error rates by incorporating improvisations on the BB84 protocol. Experimental results indicate the successful integration of the B92 error correction scheme into the modified BB84 protocol, enhancing the security and performance of QKD systems.

International Conference on Quantum Technologies, Communications, Computing, Hardware and Embedded Systems Security (iQ-CCHESS)•Sep 15, 2023•5 citations

Proof of unconditional security of six-state quantum key distribution scheme

Hoi‐Kwong Lo

We prove the unconditional security of the standard six-state scheme for quantum key distribution (QKD). We demonstrate its unconditional security up to a bit error rate of 12.7 percents, by allowing only one-way classical communications in the error correction/privacy amplification procedure between Alice and Bob. This shows a clear advantage of the six-state scheme over another standard scheme---BB84, which has been proven to be secure up to only about 11 percents, if only one-way classical communications are allowed. Our proof technique is a generalization of that of Shor-Preskill's proof of security of BB84. We show that a advantage of the six-state scheme lies in the Alice and Bob's ability to establish rigorously from their test sample the non-trivial mutual information between the bit-flip and phase error patterns. A modified version of the degenerate quantum codes studied by DiVincenzo, Shor and Smolin is employed in our proof.

arXiv:quant-ph/0102138•Feb 27, 2001•3 citations

Asymptotically Optimal Quantum Key Distribution Protocols.

Hao Shu

Quantum key distribution(QKD) could be the most significant application of quantum information theory. In nearly four decades, although substantial QKD protocols are developed, the BB84 protocol and its variants are still the most researched ones. It is well-known that the secure bound of qubit error rate(QBER) of BB84 protocol is about 11$\%$ while it can be increased to 12.6$\%$ by six-state protocol. It would not be surprising that employing more basis could increase the bound. However, what is the optimal one? In this paper, investigations of asymptotically optimal QKD protocols are proposed. Precisely, We present an abstraction of prepare-measure QKD protocols and investigate two special cases which are optimal among all protocols coding by the same states. Our analyses demonstrate that the asymptotically optimal QBER bounds coding by orthogonal qubits are about 22.17$\%$ for both general and memoryless attacks while the bounds coding by non-orthogonal states in two mutually unbiased basis are about 25.30$\%$ for general attacks and 27.00$\%$ for memoryless attacks. The significant improvement indicates the huge space for previous protocols to improve their security while the optimality of our protocols demonstrates the ultimate potential of their security.

•Oct 5, 2021•2 citations
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.
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, {\em Physical Review Letters}, 100:170502] 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.
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.
Local randomization is a preprocessing procedure in which one of the legitimate parties of a quantum key distribution (QKD) scheme adds noise to their version of the key and was found by Kraus et al. [Phys. Rev. Lett. 95, 080501 (2005)] to improve the security of certain QKD protocols. In this article, the improvement yielded by local randomization is derived for an imperfect implementation of the Bennett-Brassard 1984 (BB84) QKD protocol, in which the source emits four given but arbitrary pure states and the detector performs arbitrarily aligned measurements. Specifically, this is achieved by modifying an approach to analyzing the security of imperfect variants of the BB84 protocol against collective attacks, introduced in [Phys. Rev. A 88, 012331 (2013)], to include the additional preprocessing step. The previously known improvement to the threshold channel noise, from 11% to 12.41%, is recovered in the special case of an ideal BB84 implementation and becomes more pronounced in the case of a nonideal source. Finally, the bound derived for the asymptotic key rate, both with and without local randomization, is shown to be tight with the particular source characterization used. This is demonstrated by the explicit construction of a family of source states and optimal attacks for which the key-rate bound is attained with equality.
Quantum key distribution (QKD) is a method that enables secure communication between two parties by applying the ideas of quantum physics. By minimizing information leakage that can happen during the key generation process, privacy amplification is a technique used to improve the security of QKD. The technique involves processing the raw key obtained from QKD through a randomization procedure to remove any residual information that may have been leaked during the quantum transmission. While privacy amplification can significantly improve the security of QKD, the effectiveness of the technique is limited by the quality of the initial raw key. The BB84 QKD protocol has been improved with the proposed En-BB84 protocol, which includes built-in authentication and integrity checks. The En-BB84 protocol ensures secure distribution of secret keys and protects against tampering by attackers. Key distillation and error correction techniques are employed to extract a shorter, more secure shared secret key and correct errors introduced during qubit transmission. The protocol utilizes a four-state QKD approach, expanding on the traditional two-state scheme of BB84. A simulation of the En-BB84 protocol is demonstrated using a quantum circuit implemented with Qiskit in Python. The circuit employs various gates and operations, including Hadamard, CX, controlled swap, and RZ gates, to achieve encoding and error correction. Furthermore, we have designed a better protocol with improved error rates by incorporating improvisations on the BB84 protocol. Experimental results indicate the successful integration of the B92 error correction scheme into the modified BB84 protocol, enhancing the security and performance of QKD systems.
We prove the unconditional security of the standard six-state scheme for quantum key distribution (QKD). We demonstrate its unconditional security up to a bit error rate of 12.7 percents, by allowing only one-way classical communications in the error correction/privacy amplification procedure between Alice and Bob. This shows a clear advantage of the six-state scheme over another standard scheme---BB84, which has been proven to be secure up to only about 11 percents, if only one-way classical communications are allowed. Our proof technique is a generalization of that of Shor-Preskill's proof of security of BB84. We show that a advantage of the six-state scheme lies in the Alice and Bob's ability to establish rigorously from their test sample the non-trivial mutual information between the bit-flip and phase error patterns. A modified version of the degenerate quantum codes studied by DiVincenzo, Shor and Smolin is employed in our proof.
Quantum key distribution(QKD) could be the most significant application of quantum information theory. In nearly four decades, although substantial QKD protocols are developed, the BB84 protocol and its variants are still the most researched ones. It is well-known that the secure bound of qubit error rate(QBER) of BB84 protocol is about 11%\%% while it can be increased to 12.6%\%% by six-state protocol. It would not be surprising that employing more basis could increase the bound. However, what is the optimal one? In this paper, investigations of asymptotically optimal QKD protocols are proposed. Precisely, We present an abstraction of prepare-measure QKD protocols and investigate two special cases which are optimal among all protocols coding by the same states. Our analyses demonstrate that the asymptotically optimal QBER bounds coding by orthogonal qubits are about 22.17%\%% for both general and memoryless attacks while the bounds coding by non-orthogonal states in two mutually unbiased basis are about 25.30%\%% for general attacks and 27.00%\%% for memoryless attacks. The significant improvement indicates the huge space for previous protocols to improve their security while the optimality of our protocols demonstrates the ultimate potential of their security.