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Quantum Key Distribution (QKD) provides information-theoretic security by exploiting the principles of quantum mechanics. Among QKD protocols, the BB84 scheme remains the most widely adopted for both theoretical research and practical…

Quantum Physics · Physics 2026-03-31 Jaydeep Rath , Prajwal Panth , P. S. N. Bhaskar

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…

Quantum Physics · Physics 2007-05-23 Tim Meyer , Hermann Kampermann , Matthias Kleinmann , Dagmar Bruss

We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the source and detector are under the limited control of an adversary. Our proof applies when both the source and the detector have…

Quantum Physics · Physics 2007-05-23 Daniel Gottesman , Hoi-Kwong Lo , Norbert Lütkenhaus , John Preskill

We present a finite-size security proof of the decoy-state BB84 QKD protocol against coherent attacks, using entropic uncertainty relations, for imperfect detectors. We apply this result to the case of detectors with imperfectly…

Quantum Physics · Physics 2025-12-16 Devashish Tupkary , Shlok Nahar , Pulkit Sinha , Norbert Lütkenhaus

We propose an efficient four-intensity decoy-state BB84 protocol and derive concise security bounds for this protocol with the universally composable finite-key analysis method. Comparing with the efficient three-intensity protocol, we find…

Quantum Physics · Physics 2016-03-16 Haodong Jiang , Ming Gao , Bao Yan , Weilong Wang , Zhi Ma

A central goal in information theory and cryptography is finding simple characterizations of optimal communication rates subject to various restrictions and security requirements. Ideally, the optimal key rate for a quantum key distribution…

Quantum Physics · Physics 2012-03-28 Graeme Smith , Joseph M. Renes , John A. Smolin

We present a detailed security analysis of a d-dimensional quantum key distribution protocol based on two and three mutually unbiased bases (MUBs) both in an asymptotic and finite key length scenario. The finite secret key rates are…

Quantum Physics · Physics 2016-07-21 Kamil Bradler , Mohammad Mirhosseini , Robert Fickler , Anne Broadbent , Robert Boyd

Error mitigation is one of the key challenges in realising the full potential of quantum cryptographic protocols. Consequently, there is a lot of interest in adapting techniques from quantum error correction (QEC) to improve the robustness…

Quantum Physics · Physics 2022-10-12 Shashank Kumar Ranu , Anil Prabhakar , Prabha Mandayam

The security of finite-length keys is essential for the implementation of device-independent quantum key distribution (DIQKD). Presently, there are several finite-size DIQKD security proofs, but they are mostly focused on standard DIQKD…

We present a tight security analysis of the Bennett-Brassard 1984 protocol taking into account the finite size effect of key distillation, and achieving unconditional security. We begin by presenting a concise analysis utilizing the normal…

Quantum Physics · Physics 2015-05-28 Masahito Hayashi , Toyohiro Tsurumaru

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

In this paper, we derive key-rate expressions for different quantum key distribution protocols. Our key-rate equations utilize multiple channel statistics, including those gathered from mismatched measurement bases - i.e., when Alice and…

Quantum Physics · Physics 2017-06-16 Walter O. Krawec

Currently most progresses on quantum secret sharing suffer from rate-distance bound, and thus the key rates are limited. In addition to the limited key rate, the technical difficulty and the corresponding cost together prevent large-scale…

Quantum Physics · Physics 2023-10-09 Chen-Long Li , Yao Fu , Wen-Bo Liu , Yuan-Mei Xie , Bing-Hong Li , Min-Gang Zhou , Hua-Lei Yin , Zeng-Bing Chen

We suggest that the randomness of the choices of measurement basis by Alice and Bob provides an additional important resource for quantum cryptography. As a specific application, we present a novel protocol for quantum key distribution…

Quantum Physics · Physics 2016-08-16 Hannes R. Böhm , Paul S. Böhm , Markus Aspelmeyer , Časlav Brukner , Anton Zeilinger

We provide a general formalism to characterize the cryptographic properties of quantum channels in the realistic scenario where the two honest parties employ prepare and measure protocols and the known two-way communication reconciliation…

Quantum Physics · Physics 2010-09-23 Joonwoo Bae , Antonio Acin

The six-state protocol is a discrete-variable protocol for quantum key distribution, that permits to tolerate a noisier channel than the BB84 protocol. In this work we provide a lower bound on the maximum achievable key rate of a practical…

Quantum Physics · Physics 2011-11-14 Silvestre Abruzzo , Markus Mertz , Hermann Kampermann , Dagmar Bruß

BB84-based quantum key distribution system is limited in high speed and chip integration due to the requirement of four states preparation and measurement. Recently, the simplified BB84 protocol with only three states preparation and…

Quantum Physics · Physics 2020-06-19 Hua-Lei Yin , Zeng-Bing Chen

We consider a variant of the BB84 protocol for quantum cryptography, the prototype of tomographically incomplete protocols, where the key is generated by one-way communication rather than the usual two-way communication. Our analysis,…

Quantum Physics · Physics 2011-03-15 Syed M. Assad , Jun Suzuki , Berthold-Georg Englert

We develop a new method to quantify the secret key rate for permutation-invariant protocols for coherent attacks and finite resources. The method reduces the calculation of secret key rates for coherent attacks to the calculation for…

Quantum Physics · Physics 2015-06-05 Markus Mertz , Hermann Kampermann , Sylvia Bratzik , Dagmar Bruß

All phase-encoded BB84 implementations have signal states with unbalanced amplitudes in practice. Thus, the original security analyses a priori do not apply to them. Previous security proofs use signal tagging of multi-photon pulses to…

Quantum Physics · Physics 2020-11-03 Nicky Kai Hong Li , Norbert Lütkenhaus