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arXiv:2307.09560 · IEEE International Symposium on Information Theory (ISIT)

New Security Proof of a Restricted High-Dimensional QKD Protocol

Hasan Iqbal, Walter O. Krawec

Published Jul 7, 2024• 2 citations
arXivHTMLPDF

Abstract

High-dimensional states (HD) are promising for quantum key distribution (QKD) due to their noise tolerance and efficiency. However, creating, and measuring, HD states is technologically challenging, thus making it important to study HD-QKD protocols where Alice and Bob are restricted in their quantum capabilities. In this paper, we revisit an HD-QKD protocol, introduced in (PRA 97 (4):042347), which does not require Alice and Bob to be capable of sending and measuring in full mutually unbiased bases. The previous proof of security for this protocol has relied on numerical methods. In this work, we provide a new proof of security, enabling the key-rate evaluation beyond previous work. Furthermore, our new proof produces better results for certain channel and dimension scenarios than prior work.

DOI
10.1109/isit57864.2024.10619599

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High-dimensional states (HD) are promising for quantum key distribution (QKD) due to their noise tolerance and efficiency. However, creating, and measuring, HD states is technologically challenging, thus making it important to study HD-QKD protocols where Alice and Bob are restricted in their quantum capabilities. In this paper, we revisit an HD-QKD protocol, introduced in (PRA 97 (4):042347), which does not require Alice and Bob to be capable of sending and measuring in full mutually unbiased bases. The previous proof of security for this protocol has relied on numerical methods. In this work, we provide a new proof of security, enabling the key-rate evaluation beyond previous work. Furthermore, our new proof produces better results for certain channel and dimension scenarios than prior work.
Practical implementations of quantum key distribution (QKD) extending beyond urban areas commonly use satellite links; however, the transmission of quantum states through the Earth’s atmosphere is highly susceptible to noise, restricting its application primarily to nighttime. High-dimensional (HD) QKD offers a promising solution to this limitation by employing high-dimensionally entangled quantum states. Although experimental platforms for HD QKD exist, previous security analyses have been limited to the asymptotic regime and have either relied on impractical measurements or employed computationally demanding convex optimization tasks, restricting the security analysis to low dimensions. In this work, we bridge this gap by presenting a composable finite-size security proof against both collective and coherent attacks for a general HD QKD protocol that uses only experimentally accessible measurements. In addition to the conventional yet impractical “one-shot” key rates, we provide a practical variable-length security argument that yields significantly higher expected key rates. This approach is particularly crucial under rapidly changing and turbulent atmospheric conditions, as encountered in free-space and satellite-based QKD platforms.
Most prior semi-quantum key distribution (SQKD) protocols are designed in the context of qubits. In this paper, we proposed an SQKD protocol using ([Formula: see text]+1) quantum states in two mutually unbiased bases in the context of qudits without invoking the classical party’s measurement capability. It not only decreases the quantum states sent by quantum party by half, but also improves the efficiency of key rate than qubits do. To prove the security of present protocol, we first illustrate that the present protocol is completely robust, and then prove its unconditional security from information theoretical perspective by computing its key rate and noise tolerance against cloning-based individual attack. The unconditional security proof demonstrates that the higher dimension of quantum system is, the higher key rate can be obtained and the higher noise tolerance is allowed in depolarization channel.
Quantum key distribution (QKD) has attracted much attention due to its unconditional security. High-dimensional quantum key distribution (HD-QKD) is a brand-new type of QKD protocol that has many excellent advantages. Nonetheless, practical imperfections in realistic devices that are not considered in the theoretical security proof may have an impact on the practical security of realistic HD-QKD systems. In this paper, we research the influence of a realistic intensity modulator on the practical security of HD-QKD systems with the decoy-state method and finite-key effects. We demonstrate that there is a certain impact in the secret key rate and the transmission distance when taking practical factors into security analysis.
Time-energy high-dimensional quantum key distribution (HD-QKD) leverages the high-dimensional nature of time-energy entangled biphotons and the loss tolerance of single-photon detection to achieve long-distance key distribution with high photon information efficiency. To date, the general-attack security of HD-QKD has only been proven in the asymptotic regime, while HD-QKD's finite-key security has only been established for a limited set of attacks. Here we fill this gap by providing a rigorous HD-QKD security proof for general attacks in the finite-key regime. Our proof relies on an entropic uncertainty relation that we derive for time and conjugate-time measurements that use dispersive optics, and our analysis includes an efficient decoy-state protocol in its parameter estimation. We present numerically evaluated secret-key rates illustrating the feasibility of secure and composable HD-QKD over metropolitan-area distances when the system is subjected to the most powerful eavesdropping attack.
In this thesis we develop practical tools for quantum key distribution (QKD) security proofs. We apply the tools to provide security proofs for several protocols, ranging from discrete variable protocols in high dimensions, protocols with realistic implementations, measurement device independent QKD and continuous-variable QKD. The security proofs are based on the Devetak-Winter security framework [I. Devetak and A. Winter, Proc. of the Roy. Soc. of London Series A, 461, 207 (2005); B. Kraus, N. Gisin, and R. Renner, Phys. Rev. Lett., 95 080501 (2005)]. \n \nIn the key rate calculation, it is often convenient to assume that the optimal attack is symmetric. \nUnder the assumption that the parameter estimation is based on coarse-grained observations, we show that the optimal attack is symmetric, if the protocol and the postselection have sufficient symmetries. \nAs an example we calculate the key rates of protocols using 2, d and d+1 mutually unbiased bases in d-dimensional Hilbert spaces. \n \nWe investigate the connection between the optimal collective eavesdropping attack and the optimal cloning attack, in which the eavesdropper employs an optimal cloner to attack the protocol. \nWe find that, in general, it does not hold that the optimal attack is an optimal cloner. However, there are classes of protocols, for which we can identify the optimal attack by an optimal cloner. \nWe analyze protocols with mutually unbiased bases in d dimensions, and show that for the protocols with 2 and d+1 mutually unbiased bases the optimal attack is an optimal cloner, but for the protocols with d mutually unbiased bases, it is not. \n \nIn optical implementations of the phase-encoded BB84 protocol, the bit information is usually encoded in the phase of two consecutive photon pulses generated in a Mach-Zehnder interferometer. In the actual experimental realization, the loss in the arms of the Mach-Zehnder interferometer is not balanced, for example because only one arm contains a lossy phase modulator. \nSince the imbalance changes the structure of the signals states and measurements, the BB84 security analysis no longer applies in this scenario. \nWe provide a security proof for the unbalanced phase-encoded BB84. The loss does lower the key rate compared to a protocol without loss. However, for a realistic parameter regime, the same key rate is found by applying the original BB84 security analysis. \n \nRecently, the security of a measurement device-independent QKD setup with BB84 signal states was proven in Refs. [H.-K. Lo, M. Curty, and B. Qi, Phys. Rev. Lett., 108 (2012); S. L. Braunstein and S. Pirandola, Phys. Rev. Lett., 108 (2012)]. In this setup Alice and Bob send quantum states to an intermediate node, which performs the measurement, and is assumed to be controlled by Eve. \nWe analyze the security of a measurement device-independent QKD protocol with B92 signal states, and calculate the key rates numerically for a realistic implementation. \nBased on our security proof we were able to prove the security of the strong reference pulse B92 protocol. \n \nWe analyze the security of continuous-variable protocols using the entropic uncertainty relations established in Ref. [M. Berta, M. Christandl, R. Colbeck, J. M. Renes, and R. Renner, Nature Physics 6, 659 (2010)] to provide an estimate of the key rate based on the observed first and second moments. We analyze a protocol with squeezed coherent states and the 2-state protocol with two coherent states with opposite phases.
The idea of semi-quantum communication protocols provides a theoretical solution for the high costs of quantum resources. In this study, we propose an efficient semi-quantum key distribution protocol that allows Alice and quantum-capable restricted Bob to establish a secure key. Then, we demonstrate that the protocol is information-theoretic secure in the asymptotic scenario. As long as the channel noise is less than the noise tolerance of the protocol, Alice and Bob can withdraw a secure key. The proposed protocol has advantages over previous protocols regarding qubit efficiency and communication cost. Besides, our efficiency analysis is more fair and practical because noise factors are taken into account. Based on these features, it may have potential applications in future quantum communications.