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arXiv:2609.30874

From Received Power to Certified Secret Keys: A General Method for Bridging Classical FSO Link Budgets and Decoy-State QKD

Hasan Abbas Al-Mohammed

quant-phSubmitted Sep 25, 2026• Announced Sep 28, 2026• 0 citations
arXivHTMLPDF

Abstract

Received optical power determines photon arrival flux, but photon arrival flux does not certify a quantum key. This paper gives a deployment-independent interface from a classical free-space optical (FSO) link budget to phase-randomized weak coherent pulse BB84, decoy-state estimation, and composable finite-key postprocessing. The channel interface separates geometric collection, atmospheric extinction, residual pointing, and detector efficiency, and states when common geometric and pointing expressions are approximations. The finite-key output follows the decoy-state analysis of Lim et al., with key- and test-basis counts estimated separately and an infinite-decoy asymptotic reference. The numerical study covers a five-level attenuation sweep, basis- and vacuum-probability sensitivities, a conditional Chernoff comparison, and integer-count Monte Carlo. For $3.33 \times 10^8$ emitted pulses, the Hoeffding-based predicted one-kilobit-per-second distance limits are 2.727, 1.883, 1.472, 1.236, and 0.962 km from very clear to dense-fog parameterizations. These are conditional performance predictions, not experimental security certificates. Satellite, drone, high-altitude-platform, terrestrial, and train links enter through the same interface but require their own propagation, acquisition, and device inputs. The framework integrates established security tools into an engineering procedure without claiming a new security proof or a universal range.

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Medium-range terrestrial free-space quantum key distribution systems enable widespread secure networked communications in dense urban environments, where it would be infeasible to install a large number of short optical fibre links. Such networks need to perform over a wide range of conditions and their design has to balance key rate maximisation versus robust key generation over the greatest range of circumstances. Practicalities, such as manufacturability and deployment, further constrain the design space. Here, we examine challenges in translating experiment into engineering reality and identify efficient BB84 weak coherent pulse-decoy state protocol parameter regimes suitable for medium-range QKD systems considering likely system performance and environmental conditions.

Quantum Technology: Driving Commercialisation of an Enabling Science•Oct 6, 2021•4 citations
Received optical power determines photon arrival flux, but photon arrival flux does not certify a quantum key. This paper gives a deployment-independent interface from a classical free-space optical (FSO) link budget to phase-randomized weak coherent pulse BB84, decoy-state estimation, and composable finite-key postprocessing. The channel interface separates geometric collection, atmospheric extinction, residual pointing, and detector efficiency, and states when common geometric and pointing expressions are approximations. The finite-key output follows the decoy-state analysis of Lim et al., with key- and test-basis counts estimated separately and an infinite-decoy asymptotic reference. The numerical study covers a five-level attenuation sweep, basis- and vacuum-probability sensitivities, a conditional Chernoff comparison, and integer-count Monte Carlo. For 3.33×1083.33 \times 10^83.33×108 emitted pulses, the Hoeffding-based predicted one-kilobit-per-second distance limits are 2.727, 1.883, 1.472, 1.236, and 0.962 km from very clear to dense-fog parameterizations. These are conditional performance predictions, not experimental security certificates. Satellite, drone, high-altitude-platform, terrestrial, and train links enter through the same interface but require their own propagation, acquisition, and device inputs. The framework integrates established security tools into an engineering procedure without claiming a new security proof or a universal range.
Abstract Terrestrial free-space (FS) quantum key distribution (QKD) is ideally suited for deployment in dense urban environments. The transition from laboratory to commercial deployment, however, raises a number of important engineering and deployment issues. Here, we investigate these issues for efficient BB84 using a weak coherent pulse-decoy state protocol. We calculate expected key lengths for different environmental conditions and when the scope for optimisation of protocol parameters is restricted due to practical considerations. In particular, we find that for a fixed receiver basis choice probability, it can be advantageous to allow the transmitter to have a different basis choice probability depending on varying channel loss and background light levels. Finally, we examine the effects of pulse intensity uncertainty finding that they can dramatically reduce the key length. These results can be used to determine the loss budget for the FS optics of a QKD systems and assist in their design.
This paper develops a theoretical model for source-side implementation security in practical decoy-state quantum key distribution (QKD). The research object is a weak-coherent-pulse transmitter in which the emitted mean photon number is affected not only by the selected decoy setting, but also by semiconductor-laser dynamics, electrical drive response, intensity-modulator memory, residual optical effects, and slow drift. The transmitter is described at two modelling levels. The first layer is a nonlinear continuous-time carrier-photon-phase model used to explain physical mechanisms. The second layer is a pulse-indexed validation surrogate obtained by sampling the emitted pulse train under a declared operating regime and stroboscopic extraction rule. This distinction avoids treating a local discrete model as a globally valid replacement for nonlinear gain-switched laser dynamics. The model maps the selected intensity sequence to the actual pulse mean photon number, defines an operational memory length, and introduces vacuum-safe deviation metrics, residual-correlation diagnostics, conditional intensity laws, and photon-number probability intervals. These quantities are explicitly distinguished from composable security parameters. The security interpretation is an assumption audit: if the emitted intensity or phase statistics are history dependent, the standard decoy-state reduction to setting-independent photon-number yields and error rates is no longer automatic. The proposed framework therefore does not claim a new complete QKD security proof; it identifies measurable source quantities that must be exported to an appropriate finite-key or imperfect-source proof. The result is a mathematically traceable bridge between transmitter dynamics, source validation, and implementation-security requirements for practical decoy-state QKD systems. The objective of this paper is to develop a mathematically traceable dynamic source-deviation model for practical decoy-state QKD transmitters and to show how transmitter memory affects the assumptions used in decoy-state security analysis.
A research contribution focusing on the feasibility of the Decoy State BB84 Quantum Key Distribution (QKD) protocol over a free-space optical (FSO) link under strong and moderate solar radiance in the urban environment of Athens city, Greece for short distances up to 1km is presented. Emphasis is placed on the time varying attenuation which is introduced by various atmospheric processes and especially on the effect of strong atmospheric turbulence. We examine how these factors affect the performance of the FSO link by conducting numerical simulations of the Secure Key Rate (SKR) and evaluating the link availability.
Quantum key distribution (QKD) promises provably secure communications. In order to improve the secret key rate, combining a biased basis choice with the decoy-state method is proposed. Concomitantly, there is a basis-independent detection efficiency condition, which usually cannot be satisfied in a practical system, such as the time-phase encoding. Fortunately, this flaw has been recently removed theoretically and experimentally in the four-intensity decoy-state BB84 QKD protocol using the fact that the expected yields of single-photon states prepared in two bases stay the same for a given measurement basis. However, the security proofs do not fully consider the finite-key effects for general attacks. In this work, we provide the rigorous finite-key security bounds in the universally composable framework for the four-intensity decoy-state BB84 QKD protocol. We build a time-phase encoding system with 200 MHz clock to implement this protocol, in which the real-time secret key rate is more than 60 kbps over 50 km single-mode fiber.
In the age of information and globalisation, secure communication as well as the protection of sensitive data against unauthorised access are of utmost importance. Quantum cryptography currently provides the only way to exchange a cryptographic key between two parties in an unconditionally secure fashion. Owing to losses and noise of today's optical fibre and detector technology, at present quantum cryptography is limited to distances below a few 100 km. In principle, larger distances could be subdivided into shorter segments, but the required quantum repeaters are still beyond current technology. An alternative approach for bridging larger distances is a satellite-based system, that would enable secret key exchange between two arbitrary points on the globe using free-space optical communication. The aim of the presented experiment was to investigate the feasibility of satellite-based global quantum key distribution. In this context, a free-space quantum key distribution experiment over a real distance of 144 km was performed. The transmitter and the receiver were situated in 2500 m altitude on the Canary Islands of La Palma and Tenerife, respectively. The small and compact transmitter unit generated attenuated laser pulses, that were sent to the receiver via a 15-cm optical telescope. The receiver unit for polarisation analysis and detection of the sent pulses was integrated into an existing mirror telescope designed for classical optical satellite communications. To ensure the required stability and efficiency of the optical link in the presence of atmospheric turbulence, the two telescopes were equipped with a bi-directional automatic tracking system. Still, due to stray light and high optical attenuation, secure key exchange would not be possible using attenuated pulses in connection with the standard BB84 protocol. The photon number statistics of attenuated pulses follows a Poissonian distribution. Hence, by removing a photon from all pulses containing two or more photons, an eavesdropper could measure its polarisation without disturbing the polarisation state of the remaining pulse. In this way, he can gain information about the key without introducing detectable errors. To protect against such attacks, the presented experiment employed the recently developed method of using additional "decoy" states, i.e., the the intensity of the pulses created by the transmitter were varied in a random manner. By analysing the detection probabilities of the different pulses individually, a photon-number-splitting attack can be detected. Thanks to the decoy-state analysis, the secrecy of the resulting quantum key could be ensured despite the Poissonian nature of the emitted pulses. For a channel attenuation as high as 35 dB, a secret key rate of up to 250 bit/s was achieved. Our outdoor experiment was carried out under real atmospheric conditions and with a channel attenuation comparable to an optical link from ground to a satellite in low earth orbit. Hence, it definitely shows the feasibility of satellite-based quantum key distribution using a technologically comparatively simple system.
Medium-range terrestrial free-space quantum key distribution systems enable widespread secure networked communications in dense urban environments, where it would be infeasible to install a large number of short optical fibre links. Such networks need to perform over a wide range of conditions and their design has to balance key rate maximisation versus robust key generation over the greatest range of circumstances. Practicalities, such as manufacturability and deployment, further constrain the design space. Here, we examine challenges in translating experiment into engineering reality and identify efficient BB84 weak coherent pulse-decoy state protocol parameter regimes suitable for medium-range QKD systems considering likely system performance and environmental conditions.