Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

Optimal Protocols and Tradeoffs in Quantum Key Distribution

Joseph M. Renes

Published Jan 1, 2004• 2 citations
Publisher

Abstract

Quantum key distribution protocols based on equiangular spherical codes are introduced and a security comparison made to random and unbiased‐bases schemes in two and three dimensions. Attention is limited to intercept/resend attacks for simplicity. In each case, a general tradeoff between eavesdropper resistance and key generation speed is observed, with the largest possible spherical code found to be the most robust, inviting the question of their optimality in general.

DOI
10.1063/1.1834446

Related papers

Quantum Key Distribution Using Equiangular Spherical Codes

Joseph M. Renes

Mutually unbiased bases have been extensively studied in the literature and are simple and effective in quantum key distribution protocols, but they are not optimal. Here equiangular spherical codes are introduced as a more efficient and robust resource for key distribution. Such codes are sets of states that are as evenly spaced throughout the vector space as possible. In the case the two parties use qubits and face the intercept/resend eavesdropping strategy, they can make use of three equally-spaced states, called a \emph{trine}, to outperform the original four-state BB84 protocol in both speed and reliability. This points toward the optimality of spherical codes in arbitrary dimensions.

arXiv:quant-ph/0311106•Nov 17, 2003•1 citation

Equiangular spherical codes in quantum cryptography

Joseph M. Renes

Quantum key distribution protocols based on equiangular spherical codes are introduced and their behavior under the intercept/resend attack investigated. Such protocols offer a greater range of secure noise tolerance and speed options than protocols based on their cousins, the mutually-unbiased bases, while also enabling the determination of the channel noise rate without the need to sacrifice key bits. For fixed number of signal states in a given dimension, the spherical code protocols offer Alice and Bob more noise tolerance at the price of slower key generation rates.

arXiv:quant-ph/0409043•Quantum Information and Computation•Jan 1, 2005•48 citations

Quantum Key Distribution Using the Trine Ensemble

Joseph M. Renes

Mutually unbiased bases have been extensively studied in the literature and are simple and effective in quantum key distribution protocols, but they are not optimal. Here equiangular spherical codes are introduced as a more efficient and robust resource for key distribution. Such codes are sets of states that are as evenly spaced throughout the vector space as possible. In the case of qubits, the two parties can make use of three equally-spaced states, called a trine, to outperform the original four-state BB84 protocol in both speed and reliability. This points toward the optimality of spherical codes in arbitrary dimensions.

•Nov 17, 2003•0 citations

Equiangular quantum key distribution in more than two dimensions

Radhakrishnan Balu, Paul J. Koprowski, Kasso A. Okoudjou +2 more

Abstract We extend the spherical code-based key distribution protocols to qudits with dimensions 4 and 16 by constructing equiangular frames and their companions. We provide methods for equiangular frames in arbitrary dimensions for Alice to use and the companion frames, that have one antipode to eliminate one of the possibilities, made up of qudits with as part of Bob’s code. Non-orthogonal bases that form positive operator-valued measures can be constructed using the tools of frames (overcomplete bases of a Hilbert space), and here we apply them to key distribution that is robust due to the large size of the bases, making it hard to eavesdrop. We demonstrate a method to construct a companion frame for an equiangular tight frame for generated from the discrete Fourier transform, where p is any odd prime. The security analysis is based on the assumption of restricting possible attacks to an intercept/resend scenario, highlighting the advantages of qudit-based over qubit-based protocols.

arXiv:1810.05161•Journal of Physics A Mathematical and Theoretical•Dec 11, 2018•1 citation

Robustness of a quantum key distribution with two and three mutually unbiased bases

Filippo Caruso, Helle Bechmann-Pasquinucci, Chiara Macchiavello

We study the robustness of various protocols for quantum key distributions. We first consider the case of qutrits and study quantum protocols that employ two and three mutually unbiased bases. We then derive the optimal eavesdropping strategy for two mutually unbiased bases in dimension 4 and generalize the result to a quantum key distribution protocol that uses two mutually unbiased bases in arbitrary finite dimensions.

arXiv:quant-ph/0505146•Physical Review A•Sep 30, 2005•17 citations

Unconditional Security of a Three State Quantum Key Distribution Protocol

Jean-Christian Boileau, Kiyoshi Tamaki, Jamie Batuwantudawe +2 more

Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the Bennett-Brassard 1984 and Bennett 1992 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three-state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has been shown only for the trivial intercept-resend eavesdropping strategy. In this Letter, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.

arXiv:quant-ph/0408085•Physical Review Letters•Jan 31, 2005•84 citations
Quantum key distribution protocols based on equiangular spherical codes are introduced and a security comparison made to random and unbiased‐bases schemes in two and three dimensions. Attention is limited to intercept/resend attacks for simplicity. In each case, a general tradeoff between eavesdropper resistance and key generation speed is observed, with the largest possible spherical code found to be the most robust, inviting the question of their optimality in general.
Mutually unbiased bases have been extensively studied in the literature and are simple and effective in quantum key distribution protocols, but they are not optimal. Here equiangular spherical codes are introduced as a more efficient and robust resource for key distribution. Such codes are sets of states that are as evenly spaced throughout the vector space as possible. In the case the two parties use qubits and face the intercept/resend eavesdropping strategy, they can make use of three equally-spaced states, called a \emph{trine}, to outperform the original four-state BB84 protocol in both speed and reliability. This points toward the optimality of spherical codes in arbitrary dimensions.
Quantum key distribution protocols based on equiangular spherical codes are introduced and their behavior under the intercept/resend attack investigated. Such protocols offer a greater range of secure noise tolerance and speed options than protocols based on their cousins, the mutually-unbiased bases, while also enabling the determination of the channel noise rate without the need to sacrifice key bits. For fixed number of signal states in a given dimension, the spherical code protocols offer Alice and Bob more noise tolerance at the price of slower key generation rates.
Mutually unbiased bases have been extensively studied in the literature and are simple and effective in quantum key distribution protocols, but they are not optimal. Here equiangular spherical codes are introduced as a more efficient and robust resource for key distribution. Such codes are sets of states that are as evenly spaced throughout the vector space as possible. In the case of qubits, the two parties can make use of three equally-spaced states, called a trine, to outperform the original four-state BB84 protocol in both speed and reliability. This points toward the optimality of spherical codes in arbitrary dimensions.
Abstract We extend the spherical code-based key distribution protocols to qudits with dimensions 4 and 16 by constructing equiangular frames and their companions. We provide methods for equiangular frames in arbitrary dimensions for Alice to use and the companion frames, that have one antipode to eliminate one of the possibilities, made up of qudits with as part of Bob’s code. Non-orthogonal bases that form positive operator-valued measures can be constructed using the tools of frames (overcomplete bases of a Hilbert space), and here we apply them to key distribution that is robust due to the large size of the bases, making it hard to eavesdrop. We demonstrate a method to construct a companion frame for an equiangular tight frame for generated from the discrete Fourier transform, where p is any odd prime. The security analysis is based on the assumption of restricting possible attacks to an intercept/resend scenario, highlighting the advantages of qudit-based over qubit-based protocols.
Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the Bennett-Brassard 1984 and Bennett 1992 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three-state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has been shown only for the trivial intercept-resend eavesdropping strategy. In this Letter, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.