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arXiv:2304.09401 · Physical Review Applied

Imperfect phase randomization and generalized decoy-state quantum key distribution

Shlok Nahar, Twesh Upadhyaya, Norbert Lütkenhaus

Published Dec 18, 2023• 20 citations
arXivHTMLPDF

Abstract

Decoy-state methods are essential to perform quantum key distribution (QKD) at large distances in the absence of single-photon sources. However, the standard techniques apply only if laser pulses are used that are independent and identically distributed. Moreover, they require that the laser pulses are fully phase randomized. However, realistic high-speed QKD setups do not meet these stringent requirements. In this work, we generalize decoy-state analysis to accommodate laser sources that emit imperfectly phase-randomized states. We also develop theoretical tools to prove the security of protocols with lasers that emit pulses that are independent, but not identically distributed. These tools can be used with recent work [G. Curr\'as-Lorenzo, S. Nahar, N. L\"utkenhaus, K. Tamaki, and M. Curty, Quantum Sci. Technol. (2023)] to prove the security of laser sources with correlated phase distributions as well. We quantitatively demonstrate the effect of imperfect phase randomization on key rates by computing the key rates for a simple implementation of the three-state protocol.

DOI
10.1103/physrevapplied.20.064031

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Decoy-state methods are essential to perform quantum key distribution (QKD) at large distances in the absence of single-photon sources. However, the standard techniques apply only if laser pulses are used that are independent and identically distributed. Moreover, they require that the laser pulses are fully phase randomized. However, realistic high-speed QKD setups do not meet these stringent requirements. In this work, we generalize decoy-state analysis to accommodate laser sources that emit imperfectly phase-randomized states. We also develop theoretical tools to prove the security of protocols with lasers that emit pulses that are independent, but not identically distributed. These tools can be used with recent work [G. Curr'as-Lorenzo, S. Nahar, N. L"utkenhaus, K. Tamaki, and M. Curty, Quantum Sci. Technol. (2023)] to prove the security of laser sources with correlated phase distributions as well. We quantitatively demonstrate the effect of imperfect phase randomization on key rates by computing the key rates for a simple implementation of the three-state protocol.
Abstract The performance of quantum key distribution (QKD) is severely limited by multiphoton emissions, due to the photon-number-splitting attack. The most efficient solution, the decoy-state method, requires that the phases of all transmitted pulses are independent and uniformly random. In practice, however, these phases are often correlated, especially in high-speed systems, which opens a security loophole. Here, we address this pressing problem by providing a security proof for decoy-state QKD with correlated phases that offers key rates close to the ideal scenario. Our work paves the way towards high-performance secure QKD with practical laser sources, and may have applications beyond QKD.
Decoy-state quantum key distribution (QKD) is the most widely adopted approach for overcoming the limitations of imperfect single-photon sources. However, existing security proofs typically either neglect important device imperfections or rely on assumptions that are difficult to justify in realistic high-speed implementations, such as the independent and identically distributed nature of the emitted signals. In this work, we combine and extend several recent theoretical advances to provide a comprehensive analytical finite-key security proof for decoy-state QKD that simultaneously incorporates multiple practically relevant transmitter and receiver imperfections, including state-preparation flaws, bit and basis side-channel leakage and correlations, setting-independent intensity fluctuations, and detection-efficiency mismatches.
Abstract Decoy-state quantum key distribution (QKD) is undoubtedly the most efficient solution to handle multi-photon signals emitted by laser sources, and provides the same secret key rate scaling as ideal single-photon sources. It requires, however, that the phase of each emitted pulse is uniformly random. This might be difficult to guarantee in practice, due to inevitable device imperfections and/or the use of an external phase modulator for phase randomization in an active setup, which limits the possible selected phases to a finite set. Here, we investigate the security of decoy-state QKD when the phase is actively randomized by faulty devices, and show that this technique is quite robust to deviations from the ideal uniformly random scenario. For this, we combine a novel parameter estimation technique based on semi-definite programming, with the use of basis mismatched events, to tightly estimate the parameters that determine the achievable secret key rate. In doing so, we demonstrate that our analysis can significantly outperform previous results that address more restricted scenarios.
Quantum key distribution (QKD) promises information-theoretic security based on quantum mechanics and idealized device models. Practical implementations, however, deviate from these models due to unavoidable device imperfections, and existing security proofs fall short of capturing the complexity of real-world systems. Here we introduce a versatile numerical finite-key security framework valid against general coherent attacks and applicable to a broad class of practical QKD setups. It accommodates most relevant imperfections at both transmitter and receiver, including non-independent-and-identically-distributed (non-IID) signals arising in high-speed QKD systems due to the limited bandwidth of optical modulators, while requiring only partial characterization of the apparatuses. We demonstrate the power of our framework by proving the security of a realistic decoy-state QKD implementation with laser sources, providing a practical route towards rigorous security certification of real-world QKD setups.
The decoy-state method could effectively enhance the performance of quantum key distribution (QKD) with a practical phase randomized weak coherent source. Although active modulation of the source intensity is effective and has been implemented in many experiments, passive preparation of decoy states is also an important addition to the family of decoy-state QKD protocols. In this paper, following the theory of Curty et al. [Phys. Rev. A 81, 022310 (2010)], we experimentally demonstrate the phase-encoding passive-decoy-state QKD with only linear optical setups and threshold single-photon detectors. In our experiment, two homemade independent pulsed lasers, with visibility of Hong-Ou-Mandel interference $0.53(\ifmmode\pm\else\textpm\fi{}0.003)$, have been implemented and used to passively generate the different decoy states. Finally, a secret key rate of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$/pulse is obtained with 10-km commercial fiber between Alice and Bob.
The decoy-state method in quantum key distribution (QKD) is a popular technique to approximately achieve the performance of ideal single-photon sources by means of simpler and practical laser sources. In high-speed decoy-state QKD systems, however, intensity correlations between succeeding pulses leak information about the users' intensity settings, thus invalidating a key assumption of this approach. Here, we solve this pressing problem by developing a general technique to incorporate arbitrary intensity correlations to the security analysis of decoy-state QKD. This technique only requires to experimentally quantify two main parameters: the correlation range and the maximum relative deviation between the selected and the actually emitted intensities. As a side contribution, we provide a non-standard derivation of the asymptotic secret key rate formula from the non-asymptotic one, in so revealing a necessary condition for the significance of the former.