The discrete-variables (DV) time-frequency (TF) quantum key distribution (QKD) protocol is a BB84-like protocol, which utilizes time and frequency as complementary bases. As orthogonal modulations, pulse position modulation (PPM) and frequency shift keying (FSK) are capable of transmitting several bits per symbol, i.e., per photon. However, unlike traditional binary polarization shift keying, PPM and FSK do not allow perfectly complementary bases. So information is not completely deleted when the wrong-basis filters are applied. Since a general security proof does not yet exist, we numerically assess DV-TF-QKD. We show that the secret key rate increases with a higher number of symbols per basis. Further we identify the optimal pulse relations in the two bases in terms of key rate and resistance against eavesdropping attacks.
The discrete-variables (DV) time-frequency (TF) quantum key distribution (QKD) protocol is a BB84-like protocol, which utilizes time and frequency as complementary bases. As orthogonal modulations, pulse position modulation (PPM) and frequency shift keying (FSK) are capable of transmitting several bits per symbol, i.e., per photon. However, unlike traditional binary polarization shift keying, PPM and FSK do not allow perfectly complementary bases. So information is not completely deleted when the wrong-basis filters are applied. Since a general security proof does not yet exist, we numerically assess DV-TF-QKD. We show that the secret key rate increases with a higher number of symbols per basis. Further we identify the optimal pulse relations in the two bases in terms of key rate and resistance against eavesdropping attacks.
Data encryption has become crucial in modern communication. Complex encryption algorithms are commonly used with the disadvantage that, with fast enough classical computers or not yet usable quantum computers, decryption is possible. Quantum key distribution (QKD) offers however unconditional security. This paper describes an innovative QKD protocol, the time-frequency (TF) BB84-like protocol, and discusses its ability to distribute an unconditionally secure key at a high data rate, particularly with regard to free-space links.
Quantum Key Distribution (QKD) provides information-theoretic security based on the laws of quantum mechanics, making it a promising candidate for secure communication in a post-quantum future. However, the gap between the theoretical security proofs and practical implementations introduces vulnerabilities that a capable adversary can exploit without disturbing the quantum channel. This thesis investigates such vulnerabilities within the framework of discrete-variable (DV) QKD, with a particular focus on the BB84 protocol with time-bin encoding. A simulation of a Trojan-Horse Attack (THA) targeting a time-bin BB84 transmitter is implemented in Lumerical Interconnect simulation software. In the attack, an eavesdropper injects bright light through the quantum channel using time-multiplexing at the protocol wavelength. The back-reflected light, carrying phase information from Alice’s phase modulator, is analyzed using homodyne detection. The simulation demonstrates that all four BB84 states are distinguishable at a base signal attenuation of 30 dB. Between 30 dB and 70 dB, the signatures gradually become more suppressed, providing full or partial state preparation information. At 70 dB total signal attenuation, the state preparation signatures are fully suppressed by the shot noise, establishing a practical security threshold for this attack scenario. At intermediate attenuation levels where individual state identification becomes ambiguous while basis information remains extractable, a combined basis-informed intercept-and-resend attack is possible without raising the quantum bit error rate. The 70 dB threshold is shown to be achievable in practice through the combined use of optical isolators, anti-reflective optical connections, and careful placement of Alice’s attenuator after the phase modulator. While the classical quadrature measurement is suppressed at this level, a rigorous security analysis cannot exclude the possibility of phase information carried by individual back-reflected photons being measured. The residual back-reflected photon number must, therefore, be treated as a leakage parameter in the security proof, with privacy amplification increased to account for an adversary’s potential information gain.
We study large-alphabet quantum key distribution (QKD) based on the use of weak-coherent states and the time–frequency uncertainty relation. The large alphabet is achieved by dividing time and spectrum into M bins resulting in a frame similar to traditional pulse-position modulation (in time domain). However, the non-uniform occurrence of a photon prepared in a time/frequency bin creates the space for eavesdropping. By analysis, we show that a new intercept-resend attack strategy exists, which is stronger than that has been reported in the literature and hence the secret key rate of time-frequency QKD (TF-QKD) can be more tightly bounded. We then analyse the secret key rates of TF-QKD under various practical issues, such as channel loss, background noise, jitter and atmospheric turbulence in order to better understand the applicability of TF-QKD. Further, we discuss the information reconciliation for TF-QKD. Specifically, we investigate the layered coding scheme for TF-QKD based on quasi-cyclic low-density parity-check codes against jitter and atmospheric turbulence. By simulation, we demonstrate that information reconciliation can be efficiently achieved.
Abstract Twin-field quantum key distribution (TF-QKD) and its variant protocols are highly attractive due to the advantage of overcoming the rate-loss limit for secret key rates of point-to-point QKD protocols. For variations of TF-QKD, the key point to ensure security is switching randomly between a code mode and a test mode. Among all TF-QKD protocols, their code modes are very different, e.g. modulating continuous phases, modulating only two opposite phases, and sending or not sending signal pulses. Here we show that, by discretizing the number of global phases in the code mode, we can give a unified view on the first two types of TF-QKD protocols, and demonstrate that increasing the number of discrete phases extends the achievable distance, and as a trade-off, lowers the secret key rate at short distances due to the phase post-selection.
The bases traditionally used for quantum key distribution (QKD) are a 0 or pi/2 polarization or alternatively a 0 or pi/2 phase measured by interferometry. We introduce a new set of bases, i.e. pulses sent in either a frequency or time basis if the pulses are assumed to be transform limited. In addition it is discussed how this scheme can be easily generalized from a binary to an N-dimensional system, i.e., to ``quNdits.'' Optimal pulse distribution and the chances for eavesdropping are discussed.
Die Quantenschlüsselverteilung (QKD), die erste anwendbare Quantentechnologie, verspricht informationstheoretisch sichere Kommunikation. In der vorliegenden Arbeit wurde das Zeit-Frequenz (TF)-QKD-Protokoll untersucht, das Zeit und Frequenz, nämlich Puls-Positionsmodulation (PPM) im Zeitbereich und Frequenzumtastung (FSK) im Frequenzbereich als die beiden komplementären Basen verwendet. Seine Sicherheit beruht den Quanteneigenschaften von Licht und auf der Zeit-Frequenz-Unschärferelation. TF-QKD kann mit größtenteils Standard-Telekommunikationstechnologie im 1550-nm-Band implementiert werden. Die PPM-Basis kann mit Modulatoren und die FSK-Basis mit Hilfe der Wellenlängenmultiplex-Technologie realisiert werden. Das TF-QKD-Protokoll ist in der Lage, ein beliebig großes Alphabet bereitzustellen, was mehr als 1 bit/Photon ermöglicht. Darüber hinaus ist es robust gegenüber athmosphärischen Störungen und somit für die Übertragung über den Freiraumkanal geeignet. In der vorliegenden Arbeit wird das TF-QKD-Protokoll theoretisch bewertet, mit Standardkomponenten für 1 bit/Photon implementiert und die Freiraumübertragung mit optischem Tracking über eine 388 m Teststrecke wird bei Tageslicht demonstriert. Unter Verwendung der vorhandenen Komponenten konnte eine sichere Schlüsselrate von 364 kbit/s back-to-back und 9 kbit/s über den Freiraumkanal demonstriert werden.