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Verhandlungen der Deutschen Physikalischen Gesellschaft

Spectral effects in quantum key distribution

Wolfram Helwig, Wolfgang Mauerer, Christine Silberhorn

Published Jul 1, 2008• 0 citations
OpenAlex

Abstract

In recent years tremendous research progress was made in the field of quantum key distribution (QKD). By now a variety of protocols exists for which security has been proven even for realistic imperfect devices. The proofs based on the idea of Shor and Preskill, provide us with a lower bound on the secure key generation rate. The security of BB84 relies on the fact, that well defined single-mode photonic states are prepared by the sender and used as information carriers. However, potential sources for QKD implementations like parametric down conversion (PDC) sources emit states with a multi-mode spectral distribution. These states have to be described in a higher-dimensional Hilbert space. We investigate to what extent these spectral properties affect the security considerations. We further present a comparison of the theoretical bounds on the secure key rates for different protocols and the dependence on various experimental imperfections, e.g., dark-counts, detector efficiency, channel attenuation etc. Only single-photon signals contribute to the secure key, but unfortunately such sources don't exist at present. Hence we consider different photon statistics in our simulations.

Related papers

Multimode states in decoy-based quantum-key-distribution protocols

Wolfram Helwig, Wolfgang Mauerer, Christine Silberhorn

Every security analysis of quantum-key distribution (QKD) relies on a faithful modeling of the employed quantum states. Many photon sources, such as for instance a parametric down-conversion (PDC) source, require a multimode description but are usually only considered in a single-mode representation. In general, the important claim in decoy-based QKD protocols for indistinguishability between signal and decoy states does not hold for all sources. We derive bounds on the single-photon transmission probability and error rate for multimode states and apply these bounds to the output state of a PDC source. We observe two opposing effects on the secure key rate. First, the multimode structure of the state gives rise to a new attack that decreases the key rate. Second, more contributing modes change the photon number distribution from a thermal toward a Poissonian distribution, which increases the key rate.

arXiv:0901.4695•Physical Review A•Nov 19, 2009•16 citations

Experimental quantum cryptography with single photons and imperfect devices

Aodhán Corrigan, Koray Kaymazlar, Zhiyao Wang +9 more

Quantum key distribution (QKD) allows for provably secure key distribution between two trusted parties. Because the security and performance of QKD protocols rely on devices that behave according to specific assumptions, idealized or inaccurate assumptions about device behavior can introduce security loopholes. Real devices can never be perfectly characterized, and their performance metrics are always subject to certain error margins, which must be accounted for in a rigorous theoretical analysis. Only recently have rigorous finite-size results allowed for imperfect characterizations of devices (where device parameter have uncertainty margins) - an advance yet to be considered in experimental implementations of the BB84 protocol. In this work, we prove the security and analyze the performance of an implementation of the BB84 protocol using single photons generated by a semiconductor quantum dot light source in combination with dynamic polarization-state encoding. We consider the presence of incompletely characterized devices by accounting for imperfections in the single-photon source (in terms of finite g(2)(0)) as well as the receiver (non-ideal beam-splitters, finite detector efficiencies, and dark counts), all with error margins. The resulting protocol implementation shows competitive performance, paving the way towards practical and loop-hole free implementations of QKD.

quant-pharXiv:2607.19204•Jul 22, 2026•0 citations

Quantum communication with spectrally correlated photons (Conference Presentation)

Piotr Leszek Kolenderski, Mikołaj Lasota, Karolina Sedziak +1 more

Single-photon sources are crucial components for the implementation of quantum communication protocols. However, photons emitted by some of the most popular types of realistic sources are spectrally broadband. Due to this drawback, the signal emitted from such sources is typically affected by the effect of temporal broadening during its propagation through telecommunication fibers which exhibit chromatic dispersion. Such problem can be observed e.g. when using sources based on the process of spontaneous parametric down-conversion (SPDC). In the case of long-distance quantum communication temporal broadening can significantly limit the efficiency of temporal filtering. It is a popular method, which is based on the reduction of the duration time of the detection window, used for decreasing the number of registered errors. In this work we analyzed the impact of the type of spectral correlation within a pair of photons produced by the SPDC source on the temporal width of those photons during their propagation in dispersive media. We found out that in some situations the width can be decreased by changing the typical negative spectral correlation into positive one or by reducing its strength. This idea can be used to increase the efficiency of the temporal filtering method. Therefore it can be applied in various implementations of quantum communication protocols. As an example of the application we subsequently analyzed the security of a quantum key distribution (QKD) scheme based on single photons. It was realized in the configuration with the source of photons located in the middle between the legitimate participants of a QKD protocol (called typically Alice and Bob). We demonstrated that when the information about the emission time of the photons produced by the SPDC source is not distributed to Alice and Bob, the maximal security distance can be considerably extended by using positively correlated photons, while in the opposite case strongly (no matter positively or negatively) correlated photons are optimal. We also found out that the results of our calculation may be very sensitive to the spectral widths of the photons produced by the SPDC source. In addition, we concluded that in realistic situation Alice and Bob would have to optimize their source over both the spectral widths of the generated photons and the type of spectral correlation in order to maximally extend the security distance. The results of our work are, in particular, important for the QKD systems utilizing commercial telecom fibers populated by strong classical signals. In those systems temporal filtering method can be used to reduce not only the dark counts registered by the detection system, but also the channel noise originating from the process of Raman scattering, which is the main factor limiting their performance.

Quantum Communications and Quantum Imaging•Sep 19, 2017•0 citations

Impact of Physical Channel Impairments and Detector Noise on BB84 Quantum Key Distribution: A Python-Based Simulation Study

Avinash Upadhyay, Shashwat Saxena, Ritu Raj Singh +3 more

The absence of real single-photon sources is a significant limitation to the experimental implementation of the BB84 quantum key distribution (QKD) protocol. When substantially attenuated laser pulses are substituted for ideal sources in practical systems, the outcome is weak coherent states where each pulse has a nonzero probability of having multiple photons rather than pure single-photon emission. To evaluate quantum bit error rate (QBER), key generation rate and overall system security it is essential to describe the exact impact of the optical and physical system on such pulses. This practical tradeoff presents additional issues. It is crucial to understand how QBER is impacted by attenuation, loss, dispersion, depolarisation and detector properties particularly in adversarial scenarios such as photon number splitting (PNS) and beam-splitting attacks. Although a significant amount of research has been conducted on algorithmic simulations of BB84, there are few complete frameworks that can physically explain these effects and their impact on QBER. This work models the BB84 protocol at the physical level by developing a Python-based simulation platform that takes into account all significant channel impairments and system inefficiencies. The framework supports both theoretical and practical optimisation of QKD systems by further isolating the effects of different optical losses and eavesdropping techniques on QBER and secure key generation.

National Conference on Communications•Feb 26, 2026•1 citation

Non-Gaussianity and security of entanglement-based QKD

Mariia Gumberidze, Vladyslav C. Usenko

We theoretically analyse the relation between non-Gaussianity and security of entanglement-based quantum key distribution (QKD) protocols, namely device-independent (DI) and entanglement-based BB$84$. A similar analysis has already been made for prepare-and-measure (P\&M) protocols \cite{Lasota2017}. In addition, we consider imperfect detection with dark counts and limited efficiency. We assume a perfect source of entangled Bell states as produced by quantum-dot type sources, depolarisation in the channel and different noise statistics, namely thermal and Poissonian. We consider single-photon avalanche photodiodes (SPAD) and photon number resolving detectors (PNRD) and use their respective criteria for non-Gaussianity. The results show cross-regions for both security and non-Gaussianity, hence, the possibility to conclude about the suitability of a given channel for secret key distribution. Our results can be useful as a pre-check for the implementation of QKD protocols.

quant-pharXiv:2511.01761•Nov 4, 2025•0 citations

Quantum Cryptography: From Theory to Practice

Xiongfeng Ma

Quantum cryptography or quantum key distribution (QKD) applies fundamental laws of quantum physics to guarantee secure communication. The security of quantum cryptography was proven in the last decade. Many security analyses are based on the assumption that QKD system components are idealized. In practice, inevitable device imperfections may compromise security unless these imperfections are well investigated.\n\nA highly attenuated laser pulse which gives a weak coherent state is widely used in QKD experiments. A weak coherent state has multi-photon components, which opens up a security loophole to the sophisticated eavesdropper. With a small adjustment of the hardware, we will prove that the decoy state method can close this loophole and substantially improve the QKD performance. We also propose a few practical decoy state protocols, study statistical fluctuations and perform experimental demonstrations. Moreover, we will apply the methods from entanglement distillation protocols based on two-way classical communication to improve the decoy state QKD performance. Furthermore, we study the decoy state methods for other single photon sources, such as triggering parametric down-conversion (PDC) source. Note that our work, decoy state protocol, has attracted a lot of scientific and media interest. The decoy state QKD becomes a standard technique for prepare-and-measure QKD schemes.\n\nAside from single-photon-based QKD schemes, there is another type of scheme based on entangled photon sources. A PDC source is commonly used as an entangled photon source. We propose a model and post-processing scheme for the entanglement-based QKD with a PDC source. Although the model is proposed to study the entanglement-based QKD, we emphasize that our generic model may also be useful for other non-QKD experiments involving a PDC source. By simulating a real PDC experiment, we show that the entanglement-based QKD can achieve longer maximal secure distance than the single-photon-based QKD schemes.\n\nWe propose a time-shift attack that exploits the efficiency mismatch of two single photon detectors in a QKD system. This eavesdropping strategy can be realized by current technology. We will also discuss counter measures against the attack and study the security of a QKD system with efficiency mismatch detectors.

•Feb 26, 2009•21 citations
In recent years tremendous research progress was made in the field of quantum key distribution (QKD). By now a variety of protocols exists for which security has been proven even for realistic imperfect devices. The proofs based on the idea of Shor and Preskill, provide us with a lower bound on the secure key generation rate. The security of BB84 relies on the fact, that well defined single-mode photonic states are prepared by the sender and used as information carriers. However, potential sources for QKD implementations like parametric down conversion (PDC) sources emit states with a multi-mode spectral distribution. These states have to be described in a higher-dimensional Hilbert space. We investigate to what extent these spectral properties affect the security considerations. We further present a comparison of the theoretical bounds on the secure key rates for different protocols and the dependence on various experimental imperfections, e.g., dark-counts, detector efficiency, channel attenuation etc. Only single-photon signals contribute to the secure key, but unfortunately such sources don't exist at present. Hence we consider different photon statistics in our simulations.
Every security analysis of quantum-key distribution (QKD) relies on a faithful modeling of the employed quantum states. Many photon sources, such as for instance a parametric down-conversion (PDC) source, require a multimode description but are usually only considered in a single-mode representation. In general, the important claim in decoy-based QKD protocols for indistinguishability between signal and decoy states does not hold for all sources. We derive bounds on the single-photon transmission probability and error rate for multimode states and apply these bounds to the output state of a PDC source. We observe two opposing effects on the secure key rate. First, the multimode structure of the state gives rise to a new attack that decreases the key rate. Second, more contributing modes change the photon number distribution from a thermal toward a Poissonian distribution, which increases the key rate.
Quantum key distribution (QKD) allows for provably secure key distribution between two trusted parties. Because the security and performance of QKD protocols rely on devices that behave according to specific assumptions, idealized or inaccurate assumptions about device behavior can introduce security loopholes. Real devices can never be perfectly characterized, and their performance metrics are always subject to certain error margins, which must be accounted for in a rigorous theoretical analysis. Only recently have rigorous finite-size results allowed for imperfect characterizations of devices (where device parameter have uncertainty margins) - an advance yet to be considered in experimental implementations of the BB84 protocol. In this work, we prove the security and analyze the performance of an implementation of the BB84 protocol using single photons generated by a semiconductor quantum dot light source in combination with dynamic polarization-state encoding. We consider the presence of incompletely characterized devices by accounting for imperfections in the single-photon source (in terms of finite g(2)(0)) as well as the receiver (non-ideal beam-splitters, finite detector efficiencies, and dark counts), all with error margins. The resulting protocol implementation shows competitive performance, paving the way towards practical and loop-hole free implementations of QKD.
Single-photon sources are crucial components for the implementation of quantum communication protocols. However, photons emitted by some of the most popular types of realistic sources are spectrally broadband. Due to this drawback, the signal emitted from such sources is typically affected by the effect of temporal broadening during its propagation through telecommunication fibers which exhibit chromatic dispersion. Such problem can be observed e.g. when using sources based on the process of spontaneous parametric down-conversion (SPDC). In the case of long-distance quantum communication temporal broadening can significantly limit the efficiency of temporal filtering. It is a popular method, which is based on the reduction of the duration time of the detection window, used for decreasing the number of registered errors. In this work we analyzed the impact of the type of spectral correlation within a pair of photons produced by the SPDC source on the temporal width of those photons during their propagation in dispersive media. We found out that in some situations the width can be decreased by changing the typical negative spectral correlation into positive one or by reducing its strength. This idea can be used to increase the efficiency of the temporal filtering method. Therefore it can be applied in various implementations of quantum communication protocols. As an example of the application we subsequently analyzed the security of a quantum key distribution (QKD) scheme based on single photons. It was realized in the configuration with the source of photons located in the middle between the legitimate participants of a QKD protocol (called typically Alice and Bob). We demonstrated that when the information about the emission time of the photons produced by the SPDC source is not distributed to Alice and Bob, the maximal security distance can be considerably extended by using positively correlated photons, while in the opposite case strongly (no matter positively or negatively) correlated photons are optimal. We also found out that the results of our calculation may be very sensitive to the spectral widths of the photons produced by the SPDC source. In addition, we concluded that in realistic situation Alice and Bob would have to optimize their source over both the spectral widths of the generated photons and the type of spectral correlation in order to maximally extend the security distance. The results of our work are, in particular, important for the QKD systems utilizing commercial telecom fibers populated by strong classical signals. In those systems temporal filtering method can be used to reduce not only the dark counts registered by the detection system, but also the channel noise originating from the process of Raman scattering, which is the main factor limiting their performance.
The absence of real single-photon sources is a significant limitation to the experimental implementation of the BB84 quantum key distribution (QKD) protocol. When substantially attenuated laser pulses are substituted for ideal sources in practical systems, the outcome is weak coherent states where each pulse has a nonzero probability of having multiple photons rather than pure single-photon emission. To evaluate quantum bit error rate (QBER), key generation rate and overall system security it is essential to describe the exact impact of the optical and physical system on such pulses. This practical tradeoff presents additional issues. It is crucial to understand how QBER is impacted by attenuation, loss, dispersion, depolarisation and detector properties particularly in adversarial scenarios such as photon number splitting (PNS) and beam-splitting attacks. Although a significant amount of research has been conducted on algorithmic simulations of BB84, there are few complete frameworks that can physically explain these effects and their impact on QBER. This work models the BB84 protocol at the physical level by developing a Python-based simulation platform that takes into account all significant channel impairments and system inefficiencies. The framework supports both theoretical and practical optimisation of QKD systems by further isolating the effects of different optical losses and eavesdropping techniques on QBER and secure key generation.
We theoretically analyse the relation between non-Gaussianity and security of entanglement-based quantum key distribution (QKD) protocols, namely device-independent (DI) and entanglement-based BB848484. A similar analysis has already been made for prepare-and-measure (P\&M) protocols \cite{Lasota2017}. In addition, we consider imperfect detection with dark counts and limited efficiency. We assume a perfect source of entangled Bell states as produced by quantum-dot type sources, depolarisation in the channel and different noise statistics, namely thermal and Poissonian. We consider single-photon avalanche photodiodes (SPAD) and photon number resolving detectors (PNRD) and use their respective criteria for non-Gaussianity. The results show cross-regions for both security and non-Gaussianity, hence, the possibility to conclude about the suitability of a given channel for secret key distribution. Our results can be useful as a pre-check for the implementation of QKD protocols.
Quantum cryptography or quantum key distribution (QKD) applies fundamental laws of quantum physics to guarantee secure communication. The security of quantum cryptography was proven in the last decade. Many security analyses are based on the assumption that QKD system components are idealized. In practice, inevitable device imperfections may compromise security unless these imperfections are well investigated.\n\nA highly attenuated laser pulse which gives a weak coherent state is widely used in QKD experiments. A weak coherent state has multi-photon components, which opens up a security loophole to the sophisticated eavesdropper. With a small adjustment of the hardware, we will prove that the decoy state method can close this loophole and substantially improve the QKD performance. We also propose a few practical decoy state protocols, study statistical fluctuations and perform experimental demonstrations. Moreover, we will apply the methods from entanglement distillation protocols based on two-way classical communication to improve the decoy state QKD performance. Furthermore, we study the decoy state methods for other single photon sources, such as triggering parametric down-conversion (PDC) source. Note that our work, decoy state protocol, has attracted a lot of scientific and media interest. The decoy state QKD becomes a standard technique for prepare-and-measure QKD schemes.\n\nAside from single-photon-based QKD schemes, there is another type of scheme based on entangled photon sources. A PDC source is commonly used as an entangled photon source. We propose a model and post-processing scheme for the entanglement-based QKD with a PDC source. Although the model is proposed to study the entanglement-based QKD, we emphasize that our generic model may also be useful for other non-QKD experiments involving a PDC source. By simulating a real PDC experiment, we show that the entanglement-based QKD can achieve longer maximal secure distance than the single-photon-based QKD schemes.\n\nWe propose a time-shift attack that exploits the efficiency mismatch of two single photon detectors in a QKD system. This eavesdropping strategy can be realized by current technology. We will also discuss counter measures against the attack and study the security of a QKD system with efficiency mismatch detectors.