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Quantum key distribution (QKD) allows for communication with security guaranteed by quantum theory. The main theoretical problem in QKD is to calculate the secret key rate for a given protocol. Analytical formulas are known for protocols…

Quantum Physics · Physics 2016-05-24 Patrick J. Coles , Eric M. Metodiev , Norbert Lütkenhaus

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…

Quantum Physics · Physics 2021-01-05 Darius Bunandar , Luke C. G. Govia , Hari Krovi , Dirk R. Englund

Numerical security proofs based on conic optimization are known to deliver optimal secret-key rates, but so far they have mostly assumed that the emitted states are fully characterized. In practice, this assumption is unrealistic, since…

Quantum Physics · Physics 2025-10-30 Margarida Pereira , Guillermo Currás-Lorenzo , Mateus Araújo

Computing the key rate in quantum key distribution (QKD) protocols is a long standing challenge. Analytical methods are limited to a handful of protocols with highly symmetric measurement bases. Numerical methods can handle arbitrary…

Quantum Physics · Physics 2023-05-25 Mateus Araújo , Marcus Huber , Miguel Navascués , Matej Pivoluska , Armin Tavakoli

Finite-size general security proofs for quantum key distribution based on R\'enyi entropies have recently been introduced. These approaches are more flexible and provide tighter bounds on the secret key rate than traditional formulations…

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…

Quantum Physics · Physics 2011-10-13 Silvestre Abruzzo , Hermann Kampermann , Markus Mertz , Dagmar Bruß

In theory, quantum key distribution (QKD) provides unconditional security; however, its practical implementations are susceptible to exploitable vulnerabilities. This investigation tackles the constraints in practical QKD implementations…

Quantum key distribution (QKD) establishes secure links between remote communication parties. As a key problem for various QKD protocols, security analysis gives the amount of secure keys regardless of the eavesdropper's computational…

Quantum Physics · Physics 2023-09-26 Hongyi Zhou , Toshihiko Sasaki , Masato Koashi

In this work, we present a reliable, efficient, and tight numerical method for calculating key rates for finite-dimensional quantum key distribution (QKD) protocols. We illustrate our approach by finding higher key rates than those…

Quantum Physics · Physics 2018-07-30 Adam Winick , Norbert Lütkenhaus , Patrick J. Coles

Quantum Key Distribution (QKD) allows unconditionally secure communication based on the laws of quantum mechanics rather then assumptions about computational hardness. Optimizing the operation parameters of a given QKD implementation is…

Finite key analysis of quantum key distribution (QKD) is an important tool for any QKD implementation. While much work has been done on the framework of finite key analysis, the application to individual protocols often relies on the the…

Quantum Physics · Physics 2021-03-29 Ian George , Jie Lin , Norbert Lütkenhaus

With the rise of quantum technologies, data security increasingly relies on quantum cryptography and its most notable application, quantum key distribution (QKD). Yet, current technological limitations, in particular, the unavailability of…

Quantum cryptography has attracted much attention in recent years. In most existing quantum cryptographic protocols, players usually need the full quantum power of generating, manipulating or measuring quantum states. Semiquantum…

Quantum Physics · Physics 2018-11-12 Ming-Ming Wang , Lin-Ming Gong , Lian-He Shao

Quantum key distribution (QKD) protocols aim at allowing two parties to generate a secret shared key. While many QKD protocols have been proven unconditionally secure in theory, practical security analyses of experimental QKD…

Quantum Physics · Physics 2023-07-04 Michel Boyer , Gilles Brassard , Nicolas Godbout , Rotem Liss , Stéphane Virally

We propose a schematic setup of quantum key distribution (QKD) with an improved secret key rate based on high-dimensional quantum states. Two degrees-of-freedom of a single photon, orbital angular momentum modes, and multi-path modes, are…

Quantum Physics · Physics 2019-01-29 Yonggi Jo , Hee Su Park , Seung-Woo Lee , Wonmin Son

We calculate an achievable secret key rate for quantum key distribution with a finite number of signals, by evaluating the min-entropy explicitly. The min-entropy can be expressed in terms of the guessing probability, which we calculate for…

Quantum Physics · Physics 2011-03-22 Sylvia Bratzik , Markus Mertz , Hermann Kampermann , Dagmar Bruß

Modern security proofs of quantum key distribution (QKD) must take finite-size effects and composable aspects into consideration. This is also the case for continuous-variable (CV) protocols which are based on the transmission and detection…

Quantum Physics · Physics 2025-11-27 Stefano Pirandola , Panagiotis Papanastasiou

Practical quantum key distribution (QKD) protocols require a finite-size security proof. The phase error correction (PEC) approach is one of the general strategies for security analyses that has successfully proved finite-size security for…

Quantum Physics · Physics 2026-05-15 Takaya Matsuura , Shinichiro Yamano , Yui Kuramochi , Toshihiko Sasaki , Masato Koashi

Quantum key distribution (QKD) is a cornerstone of the secure quantum encryption. Building on the quantum irreversibility, we develop a technique reborning the existing QKDs into protocols that are unrestricted in distance and have…

Security proof methods for quantum key distribution, QKD, that are based on the numerical key rate calculation problem, are powerful in principle. However, the practicality of the methods are limited by computational resources and the…

Quantum Physics · Physics 2022-09-14 Hao Hu , Jiyoung Im , Jie Lin , Norbert Lütkenhaus , Henry Wolkowicz
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