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:1503.01498 · Entropy

Finite Key Size Analysis of Two-Way Quantum Cryptography

Jesni Shamsul Shaari, Stefano Mancini

Published Apr 30, 2015• 11 citations
arXivHTMLPDF

Abstract

Quantum cryptographic protocols solve the longstanding problem of distributing a shared secret string to two distant users by typically making use of one-way quantum channel. However, alternative protocols exploiting two-way quantum channel have been proposed for the same goal and with potential advantages. Here, we overview a security proof for two-way quantum key distribution protocols, against the most general eavesdropping attack, that utilize an entropic uncertainty relation. Then, by resorting to the “smooth” version of involved entropies, we extend such a proof to the case of finite key size. The results will be compared to those available for one-way protocols showing some advantages.

DOI
10.3390/e17052723

Related papers

Security of two-way quantum key distribution

Normand J. Beaudry, Marco Lucamarini, Stefano Mancini +1 more

Quantum key distribution protocols typically make use of a one-way quantum channel to distribute a shared secret string to two distant users. However, protocols exploiting a two-way quantum channel have been proposed as an alternative route to the same goal, with the potential advantage of outperforming one-way protocols. Here we provide a strategy to prove security for two-way quantum key distribution protocols against the most general quantum attack possible by an eavesdropper. We utilize an entropic uncertainty relation, and only a few assumptions need to be made about the devices used in the protocol. We also show that a two-way protocol can outperform comparable one-way protocols.

arXiv:1301.3138•Physical Review A•Dec 2, 2013•91 citations

Security Proof of a Semi-Quantum Key Distribution Protocol: Extended Version

Walter O. Krawec

Semi-quantum key distribution protocols are designed to allow two users to establish a secure secret key when one of the two users is limited to performing certain "classical" operations. There have been several such protocols developed recently, however, due to their reliance on a two-way quantum communication channel (and thus, the attacker's opportunity to interact with the qubit twice), their security analysis is difficult and little is known concerning how secure they are compared to their fully quantum counterparts. In this paper we prove the unconditional security of a particular semi-quantum protocol. We derive an expression for the key rate of this protocol, in the asymptotic scenario, as a function of the quantum channel's noise. Finally, we will show that this semi-quantum protocol can tolerate a maximal noise level comparable to certain fully quantum protocols.

arXiv:1412.0282•Nov 30, 2014•2 citations

Entropy uncertainty relations and stability of phase-temporal quantum cryptography with finite-length transmitted strings

S. N. Molotkov

Any key-generation session contains a finite number of quantum-state messages, and it is there-fore important to understand the fundamental restrictions imposed on the minimal length of a string required to obtain a secret key with a specified length. The entropy uncertainty relations for smooth min and max entropies considerably simplify and shorten the proof of security. A proof of security of quantum key distribution with phase-temporal encryption is presented. This protocol provides the maximum critical error compared to other protocols up to which secure key distribution is guaranteed. In addition, unlike other basic protocols (of the BB84 type), which are vulnerable with respect to an attack by “blinding” of avalanche photodetectors, this protocol is stable with respect to such an attack and guarantees key security.

Journal of Experimental and Theoretical Physics•Dec 1, 2012•3 citations

Quantum Key Distribution with Imperfections: Recent Advances in Security Proofs

Patrick Andriolo, Esteban Vasquez, Elizabeth Agudelo +3 more

In contrast to classical public-key cryptosystems, where the security of encoded messages relies on on computational assumptions, Quantum Key Distribution (QKD) enables two distant parties to establish a shared secret key that, when combined with a one-time pad, provides information-theoretically secure encryption, provided that the QKD protocol is supported by a rigorous security proof. In the last decades, security proofs robust against a wide range of eavesdropping strategies have established the theoretical soundness of several QKD protocols. However, most proofs are based on idealized models of the physical systems involved in such protocols and often include assumptions that are not satisfied in practical implementations. This mismatch creates a gap between theoretical security guarantees and actual experimental realizations, making QKD protocols vulnerable to attacks. To ensure the security of real-world QKD systems, it is therefore essential to account for imperfections in security analyses. In this article, we present an overview of recent analytical and numerical developments in QKD security proofs, which provide a versatile approach for incorporating imperfections and re-establishing the security of quantum communication protocols under realistic conditions.

quant-pharXiv:2602.05057•Brazilian Journal of Physics•Feb 6, 2026•1 citation

Tight finite-key analysis for quantum cryptography

Marco Tomamichel, Charles Ci Wen Lim, Nicolas Gisin +1 more

Despite enormous theoretical and experimental progress in quantum cryptography, the security of most current implementations of quantum key distribution is still not rigorously established. One significant problem is that the security of the final key strongly depends on the number, M, of signals exchanged between the legitimate parties. Yet, existing security proofs are often only valid asymptotically, for unrealistically large values of M. Another challenge is that most security proofs are very sensitive to small differences between the physical devices used by the protocol and the theoretical model used to describe them. Here we show that these gaps between theory and experiment can be simultaneously overcome by using a recently developed proof technique based on the uncertainty relation for smooth entropies. Although they offer significant promise, practical implementations of quantum key distribution are often not as rigorous as theory predicts. This study demonstrates how two instances of such discrepancies can be resolved by taking advantage of an enotropic formulation of the uncertainty principle.

arXiv:1103.4130•Nature Communications•Jan 17, 2012•641 citations

Security proof of a semi-quantum key distribution protocol

Walter O. Krawec

Semi-quantum key distribution protocols are designed to allow two users to establish a secure secret key when one of the two users is limited to performing certain “classical” operations. There have been several such protocols developed recently, however, due to their reliance on a two-way quantum communication channel (and thus, the attacker's opportunity to interact with the qubit twice), their security analysis is difficult and little is known concerning how secure they are compared to their fully quantum counterparts. In this paper we prove the unconditional security of a particular semi-quantum protocol and derive an expression for its key rate, in the asymptotic scenario.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2015•80 citations
Quantum cryptographic protocols solve the longstanding problem of distributing a shared secret string to two distant users by typically making use of one-way quantum channel. However, alternative protocols exploiting two-way quantum channel have been proposed for the same goal and with potential advantages. Here, we overview a security proof for two-way quantum key distribution protocols, against the most general eavesdropping attack, that utilize an entropic uncertainty relation. Then, by resorting to the “smooth” version of involved entropies, we extend such a proof to the case of finite key size. The results will be compared to those available for one-way protocols showing some advantages.
Quantum key distribution protocols typically make use of a one-way quantum channel to distribute a shared secret string to two distant users. However, protocols exploiting a two-way quantum channel have been proposed as an alternative route to the same goal, with the potential advantage of outperforming one-way protocols. Here we provide a strategy to prove security for two-way quantum key distribution protocols against the most general quantum attack possible by an eavesdropper. We utilize an entropic uncertainty relation, and only a few assumptions need to be made about the devices used in the protocol. We also show that a two-way protocol can outperform comparable one-way protocols.
Semi-quantum key distribution protocols are designed to allow two users to establish a secure secret key when one of the two users is limited to performing certain "classical" operations. There have been several such protocols developed recently, however, due to their reliance on a two-way quantum communication channel (and thus, the attacker's opportunity to interact with the qubit twice), their security analysis is difficult and little is known concerning how secure they are compared to their fully quantum counterparts. In this paper we prove the unconditional security of a particular semi-quantum protocol. We derive an expression for the key rate of this protocol, in the asymptotic scenario, as a function of the quantum channel's noise. Finally, we will show that this semi-quantum protocol can tolerate a maximal noise level comparable to certain fully quantum protocols.
Any key-generation session contains a finite number of quantum-state messages, and it is there-fore important to understand the fundamental restrictions imposed on the minimal length of a string required to obtain a secret key with a specified length. The entropy uncertainty relations for smooth min and max entropies considerably simplify and shorten the proof of security. A proof of security of quantum key distribution with phase-temporal encryption is presented. This protocol provides the maximum critical error compared to other protocols up to which secure key distribution is guaranteed. In addition, unlike other basic protocols (of the BB84 type), which are vulnerable with respect to an attack by “blinding” of avalanche photodetectors, this protocol is stable with respect to such an attack and guarantees key security.
In contrast to classical public-key cryptosystems, where the security of encoded messages relies on on computational assumptions, Quantum Key Distribution (QKD) enables two distant parties to establish a shared secret key that, when combined with a one-time pad, provides information-theoretically secure encryption, provided that the QKD protocol is supported by a rigorous security proof. In the last decades, security proofs robust against a wide range of eavesdropping strategies have established the theoretical soundness of several QKD protocols. However, most proofs are based on idealized models of the physical systems involved in such protocols and often include assumptions that are not satisfied in practical implementations. This mismatch creates a gap between theoretical security guarantees and actual experimental realizations, making QKD protocols vulnerable to attacks. To ensure the security of real-world QKD systems, it is therefore essential to account for imperfections in security analyses. In this article, we present an overview of recent analytical and numerical developments in QKD security proofs, which provide a versatile approach for incorporating imperfections and re-establishing the security of quantum communication protocols under realistic conditions.
Despite enormous theoretical and experimental progress in quantum cryptography, the security of most current implementations of quantum key distribution is still not rigorously established. One significant problem is that the security of the final key strongly depends on the number, M, of signals exchanged between the legitimate parties. Yet, existing security proofs are often only valid asymptotically, for unrealistically large values of M. Another challenge is that most security proofs are very sensitive to small differences between the physical devices used by the protocol and the theoretical model used to describe them. Here we show that these gaps between theory and experiment can be simultaneously overcome by using a recently developed proof technique based on the uncertainty relation for smooth entropies. Although they offer significant promise, practical implementations of quantum key distribution are often not as rigorous as theory predicts. This study demonstrates how two instances of such discrepancies can be resolved by taking advantage of an enotropic formulation of the uncertainty principle.
Semi-quantum key distribution protocols are designed to allow two users to establish a secure secret key when one of the two users is limited to performing certain “classical” operations. There have been several such protocols developed recently, however, due to their reliance on a two-way quantum communication channel (and thus, the attacker's opportunity to interact with the qubit twice), their security analysis is difficult and little is known concerning how secure they are compared to their fully quantum counterparts. In this paper we prove the unconditional security of a particular semi-quantum protocol and derive an expression for its key rate, in the asymptotic scenario.