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Journal of Modern Optics

Impact of coarse-grained measurement with finite range on continuous-variable quantum key distribution

Tianyi Wang, Song Yu, Wanyi Gu

Published Oct 22, 2015• 1 citation
Publisher

Abstract

In continuous-variable quantum key distribution, detectors are necessarily coarse grained and of finite range. We analyze the impact of both features and demonstrate that while coarse graining adds a fixed error to the estimated excess noise, finite range degrades the estimation accuracy of both transmission and excess noise. Moreover, the inaccurate estimation due to finite range may results in secret key rate underestimation, even misjudgment of security. To compensate these consequences, tuning the modulation variance is a possible way.

DOI
10.1080/09500340.2015.1084392

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In continuous-variable quantum key distribution, detectors are necessarily coarse grained and of finite range. We analyze the impact of both features and demonstrate that while coarse graining adds a fixed error to the estimated excess noise, finite range degrades the estimation accuracy of both transmission and excess noise. Moreover, the inaccurate estimation due to finite range may results in secret key rate underestimation, even misjudgment of security. To compensate these consequences, tuning the modulation variance is a possible way.
In continuous-variable quantum information processing, detectors are necessarily coarse grained and of finite range. We discuss how, especially, the latter feature is a bug and may easily lead to overoptimistic estimates of entanglement and of security when missed data outside the detector range are ignored. We demonstrate that a straightforward worst-case analysis is sufficient to avoid false positive statements about entanglement. We show that, for our worst-case analysis, entropic separability or security criteria are much superior to variance-based criteria.
We study the impact of the finite-size effect on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, mainly considering the finite-size effect on the parameter estimation procedure. The central-limit theorem and maximum likelihood estimation theorem are used to estimate the parameters. We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI QKD protocol has the farthest transmission distance in the finite-size scenario. Finally, we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol. The overall results indicate that the finite-size effect has a great influence on the secret-key rate of the CV-MDI QKD protocol and should not be ignored.
Continuous variable quantum key distribution (CV QKD) is a promising candidate for the deployment of quantum cryptography. At present, the longest distance is limited to ∼100 km at fiber-based quantum channel. We investigated in depth the realistic rate-distance limit (RDL) of CV QKD, considering reconciliation efficiency, finite-size effect, and realistic excess noise under collective attack. It is shown that the excess noise generated on Bob's side degrades significantly the transmission distance and we verify it in experiment. The improvement in RDL by reconciliation efficiency depends on the excess noise level, considerable increase of RDL by improving the reconciliation efficiency occurs only for relative large excess noises. A convergence modulation variance, useful in calculation simplification, is found. Furthermore, we restudy the finite-size analysis and eliminates a loophole arising from the Holevo-bound information monotonicity and a safe RDL is guaranteed. Based on the revised finite-size analysis, the optimum ratio determining the amount of data used for parameter estimation is analyzed.
Unidimensional-modulation continuous-variable quantum key distribution has received considerable attention due to its simplified transmitter architecture, reduced random-number consumption, and low deployment cost. However, its security against source-side light-injection attacks remains unexplored. In this paper, the effects of such attacks on unidimensional-modulation continuous-variable quantum key distribution systems are systematically investigated. A theoretical model of quantum-state preparation at the transmitter under light-injection attacks is established, parameter estimation bias formulas are derived, the resulting degradation in the secret key rate is quantified, and the theoretical results are validated through numerical simulations. In addition, the security implications of light-injection attacks in the finite-size regime are examined. The results demonstrate that light-injection attacks cause overestimation of the channel transmittance and underestimation of excess noise. Under finite-size conditions, these attacks reduce the minimum data-block length required to achieve a positive secret key rate, thereby creating a false indication of security even when no secure key can actually be generated. These findings demonstrate that light-injection attacks constitute a serious threat to unidimensional-modulation continuous-variable quantum key distribution systems and provide an important theoretical foundation for future secure practical deployment.
Abstract We address the crucial role of noisy squeezing in security and performance of continuous-variable (CV) quantum key distribution (QKD) protocols. Squeezing has long been recognized for its numerous advantages in CV QKD, such as enhanced robustness against channel noise and loss, and improved secret key rates. However, the excess noise of the squeezed states, that unavoidably originates already from optical loss as well as other imperfections in the source, raises concerns about its potential exploitation by an eavesdropper. For the widely adopted trust assumption on the excess noise in the signal states, we confirm the stability of the protocol against the noisy squeezing in both purely attenuating as well as noisy channels in the asymptotic limit, which implies perfect parameter estimation. In the finite-size regime we show that this stability largely holds at up to 107 data points using optimal biased homodyne detection for key distribution and parameter estimation. Untrusted assumption on the noisy squeezing, on the other hand, introduces additional security bounds on the squeezing excess noise already in the asymptotic regime, which is further enforced by the finite-size effects. Additionally, we show the critical negative role of noisy squeezing in the case of atmospheric free-space channels, already in the trusted-noise and asymptotic assumptions, which emphasizes the importance of squeezing purity in the free-space quantum channels. Our results pave the way towards practical realization of squeezed-state CV QKD protocols in both fibre and free-space channels.