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

arXiv:quant-ph/0607141 · Physical Review A

Finite key analysis for symmetric attacks in quantum key distribution

Tim Meyer, Hermann Kampermann, Matthias Kleinmann, Dagmar Bruß

Published Oct 30, 2006• 26 citations
arXivHTMLPDF

Abstract

We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number $n$ of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below $n\ensuremath{\sim}{10}^{4}$, the finite key rate differs significantly from the asymptotic value for $n\ensuremath{\rightarrow}\ensuremath{\infty}$. However, for larger $n$, a good approximation of the asymptotic value is found. We also study secret key rates for protocols using higher-dimensional quantum systems.

DOI
10.1103/physreva.74.042340

Related papers

Finite-key security against coherent attacks in quantum key distribution

Lana Sheridan, Lê Phuc Thinh, Valerio Scarani

Christandl et al (2009 Phys. Rev. Lett. 102 020504) provide, in particular, the possibility of studying unconditional security in the finite-key regime for all discrete-variable protocols. We spell out this bound from their general formalism. Then, we apply it in the analysis of a recently proposed protocol (Laing et al 2010 Phys. Rev. A 82 012304). This protocol is meaningful when the alignment of Alice's and Bob's reference frames is not monitored and may vary with time. In this scenario, the notion of asymptotic key rate has hardly any operational meaning, because if one waits too long a time, the average correlations are smeared out and no security can be inferred. Therefore, finite-key analysis is necessary for finding the maximal achievable secret key rate and the corresponding optimal number of signals.

arXiv:1008.2596•New Journal of Physics•Dec 9, 2010•81 citations

Quantum key distribution with finite resources: Secret key rates via Rényi entropies

Silvestre Abruzzo, Hermann Kampermann, Markus Mertz +1 more

A realistic quantum key distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem over R\'enyi entropies. Under the assumption of collective attacks by an eavesdropper, a computable estimate of our bound for the six-state protocol is provided. This bound leads to improved key rates in comparison to previous results.

arXiv:1105.5574•Physical Review A•Sep 16, 2011•13 citations

Security Analysis of Quantum Key Distribution: Methods and Applications

Jie Lin

Quantum key distribution (QKD) can be proved to be secure by laws of quantum mechanics. In this thesis, we review security proof methods in Renner's framework and discuss numerical methods to calculate asymptotic and finite key rates. These methods are highly versatile and applicable to general device-dependent QKD protocols. We also discuss analytical tools that extend the applicability of these numerical methods. We then present the asymptotic security proof against collective attacks for a variant of the twin-field QKD protocol, which can overcome the repeaterless secret-key capacity bound. Our variant reduces the sifting cost and uses non-phase-randomized coherent states as both signals and test states. We confirm the loss scaling of this protocol. Another important family of protocols that we investigate here are discrete-modulated continuous-variable QKD protocols. They are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks. Our security proof method can provide tight asymptotic key rates. We demonstrate that the postselection of data in combination with reverse reconciliation can improve the key rates. We analyze both untrusted and trusted detector noise scenarios. Our results in the trusted detector noise scenario show that we can thus cut out most of the effect of detector noise and obtain asymptotic key rates similar to those had we access to ideal detectors. Finally, we present several simple examples to illustrate our newly developed method for the numerical finite-key analysis against the most general attacks via the entropy accumulation theorem.

•Sep 27, 2021•2 citations

Quantum key distribution with finite resources: Taking advantage of quantum noise

Markus Mertz, Hermann Kampermann, Z. Shadman +1 more

We compare the effect of different noise scenarios on the achievable rate of an ${\ensuremath{\varepsilon}}_{}$-secure key for the BB84 and the six-state protocol. We study the situation where quantum noise is added deliberately, and investigate the remarkable benefit for the finite key rate. We compare our results to the known case of added classical noise and the asymptotic key rate, i.e., in the limit of infinitely many signals. As a complementary interpretation, we show that under the realistic assumption that the noise which is unavoidably introduced by a real channel is not fully dedicated to the eavesdropper, the secret key rate increases significantly.

arXiv:1112.5542•Physical Review A•Apr 9, 2013•13 citations

Eavesdropping on counterfactual quantum key distribution with finite resources

Xingtong Liu, Bo Zhang, Jian Wang +3 more

A striking scheme called ``counterfactual quantum cryptography'' gives a conceptually new approach to accomplish the task of key distribution. It allows two legitimate parties to share a secret even though a particle carrying secret information is not, in fact, transmitted through the quantum channel. Since an eavesdropper cannot directly access the entire quantum system of each signal particle, the protocol seems to provide practical security advantages. However, here we propose an eavesdropping method which works on the scheme in a finite key scenario. We show that, for practical systems only generating a finite number of keys, the eavesdropping can obtain all of the secret information without being detected. We also present a improved protocol as a countermeasure against this attack.

Physical Review A•Aug 15, 2014•14 citations

Numerical finite-key analysis of quantum key distribution

Darius Bunandar, Luke C. G. Govia, Hari Krovi +1 more

Abstract Quantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments, however, predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite-key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime in terms of two semi-definite programs (SDPs). The first uses the relation between conditional smooth min-entropy and quantum relative entropy through the quantum asymptotic equipartition property, and the second uses the relation between the smooth min-entropy and quantum fidelity. The numerical programs are formulated under the assumption of collective attacks from the eavesdropper and can be promoted to withstand coherent attacks using the postselection technique. We then solve these SDPs using convex optimization solvers and obtain numerical calculations of finite-key rates for several protocols difficult to analyze analytically, such as BB84 with unequal detector efficiencies, B92, and twin-field QKD. Our numerical approach democratizes the composable security proofs for QKD protocols where the derived keys can be used as an input to another cryptosystem.

arXiv:1911.07860•npj Quantum Information•Dec 18, 2020•52 citations
We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number nnn of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below n\ensuremath∼104n\ensuremath{\sim}{10}^{4}n\ensuremath∼104, the finite key rate differs significantly from the asymptotic value for n\ensuremath→\ensuremath∞n\ensuremath{\rightarrow}\ensuremath{\infty}n\ensuremath→\ensuremath∞. However, for larger nnn, a good approximation of the asymptotic value is found. We also study secret key rates for protocols using higher-dimensional quantum systems.
Christandl et al (2009 Phys. Rev. Lett. 102 020504) provide, in particular, the possibility of studying unconditional security in the finite-key regime for all discrete-variable protocols. We spell out this bound from their general formalism. Then, we apply it in the analysis of a recently proposed protocol (Laing et al 2010 Phys. Rev. A 82 012304). This protocol is meaningful when the alignment of Alice's and Bob's reference frames is not monitored and may vary with time. In this scenario, the notion of asymptotic key rate has hardly any operational meaning, because if one waits too long a time, the average correlations are smeared out and no security can be inferred. Therefore, finite-key analysis is necessary for finding the maximal achievable secret key rate and the corresponding optimal number of signals.
Quantum key distribution (QKD) can be proved to be secure by laws of quantum mechanics. In this thesis, we review security proof methods in Renner's framework and discuss numerical methods to calculate asymptotic and finite key rates. These methods are highly versatile and applicable to general device-dependent QKD protocols. We also discuss analytical tools that extend the applicability of these numerical methods. We then present the asymptotic security proof against collective attacks for a variant of the twin-field QKD protocol, which can overcome the repeaterless secret-key capacity bound. Our variant reduces the sifting cost and uses non-phase-randomized coherent states as both signals and test states. We confirm the loss scaling of this protocol. Another important family of protocols that we investigate here are discrete-modulated continuous-variable QKD protocols. They are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks. Our security proof method can provide tight asymptotic key rates. We demonstrate that the postselection of data in combination with reverse reconciliation can improve the key rates. We analyze both untrusted and trusted detector noise scenarios. Our results in the trusted detector noise scenario show that we can thus cut out most of the effect of detector noise and obtain asymptotic key rates similar to those had we access to ideal detectors. Finally, we present several simple examples to illustrate our newly developed method for the numerical finite-key analysis against the most general attacks via the entropy accumulation theorem.
We compare the effect of different noise scenarios on the achievable rate of an ${\ensuremath{\varepsilon}}_{}$-secure key for the BB84 and the six-state protocol. We study the situation where quantum noise is added deliberately, and investigate the remarkable benefit for the finite key rate. We compare our results to the known case of added classical noise and the asymptotic key rate, i.e., in the limit of infinitely many signals. As a complementary interpretation, we show that under the realistic assumption that the noise which is unavoidably introduced by a real channel is not fully dedicated to the eavesdropper, the secret key rate increases significantly.
A striking scheme called ``counterfactual quantum cryptography'' gives a conceptually new approach to accomplish the task of key distribution. It allows two legitimate parties to share a secret even though a particle carrying secret information is not, in fact, transmitted through the quantum channel. Since an eavesdropper cannot directly access the entire quantum system of each signal particle, the protocol seems to provide practical security advantages. However, here we propose an eavesdropping method which works on the scheme in a finite key scenario. We show that, for practical systems only generating a finite number of keys, the eavesdropping can obtain all of the secret information without being detected. We also present a improved protocol as a countermeasure against this attack.
Abstract Quantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments, however, predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite-key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime in terms of two semi-definite programs (SDPs). The first uses the relation between conditional smooth min-entropy and quantum relative entropy through the quantum asymptotic equipartition property, and the second uses the relation between the smooth min-entropy and quantum fidelity. The numerical programs are formulated under the assumption of collective attacks from the eavesdropper and can be promoted to withstand coherent attacks using the postselection technique. We then solve these SDPs using convex optimization solvers and obtain numerical calculations of finite-key rates for several protocols difficult to analyze analytically, such as BB84 with unequal detector efficiencies, B92, and twin-field QKD. Our numerical approach democratizes the composable security proofs for QKD protocols where the derived keys can be used as an input to another cryptosystem.