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Emerging Imaging and Sensing Technologies for Security and Defence

Benchmarking entanglement-based QKD protocols in noisy channels

Mikołaj Lasota, Olena Kovalenko, Vladyslav C. Usenko

Published Oct 17, 2023• 0 citations
Publisher

Abstract

We address the efficiency and robustness of quantum key distribution (QKD) based on entangled states in conditions of noisy quantum channels. We consider schemes based on either source or detection station located in the middle or the channel, the latter configuration allowing realization of measurement-device independent QKD. In our study we focus both on discrete-variable (DV) QKD protocols utilizing direct photodetection as well as continuous-variable (CV) ones, which are based on the homodyne detection. Equivalently parametrizing the channel excess noise for both DV and CV protocols, we use robustness of an ideal CV QKD protocol as a benchmark for the entanglement-based DV QKD. We show that DV protocols typically overcome the CV ones in both source- and detector-in-the-middle setup configurations. However, this advantage can be undermined by the practical aspects on the DV protocols. Considering quantum-dot type of the DV sources of entanglement, we show the levels of pair generation and collection efficiencies needed to overcome any CV protocols. The requirements are generally compatible with the existing technologies but may require experimental efforts to achieve. Our results are essential for the practical entanglement-based QKD protocols with modern efficient sources, aimed at potential scalability in the quantum networks.

DOI
10.1117/12.2685236

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We address the efficiency and robustness of quantum key distribution (QKD) based on entangled states in conditions of noisy quantum channels. We consider schemes based on either source or detection station located in the middle or the channel, the latter configuration allowing realization of measurement-device independent QKD. In our study we focus both on discrete-variable (DV) QKD protocols utilizing direct photodetection as well as continuous-variable (CV) ones, which are based on the homodyne detection. Equivalently parametrizing the channel excess noise for both DV and CV protocols, we use robustness of an ideal CV QKD protocol as a benchmark for the entanglement-based DV QKD. We show that DV protocols typically overcome the CV ones in both source- and detector-in-the-middle setup configurations. However, this advantage can be undermined by the practical aspects on the DV protocols. Considering quantum-dot type of the DV sources of entanglement, we show the levels of pair generation and collection efficiencies needed to overcome any CV protocols. The requirements are generally compatible with the existing technologies but may require experimental efforts to achieve. Our results are essential for the practical entanglement-based QKD protocols with modern efficient sources, aimed at potential scalability in the quantum networks.
Abstract Discrete-variable (DV) and continuous-variable (CV) schemes constitute the two major families of quantum key distribution (QKD) protocols. Unfortunately, since the setup elements required by these schemes are quite different, making a fair comparison of their potential performance in particular applications is often troublesome, limiting the experimenters’ capability to choose an optimal solution. In this work we perform a general comparison of the major entanglement-based DV and CV QKD protocols in terms of their resistance to the channel noise, with the otherwise perfect setup, showing the definite superiority of the DV family. We analytically derive fundamental bounds on the tolerable channel noise and attenuation for entanglement-based CV QKD protocols. We also investigate the influence of DV QKD setup imperfections on the obtained results in order to determine benchmarks for the parameters of realistic photon sources and detectors, allowing the realistic DV protocols to outperform even the ideal CV QKD analogs. Our results indicate the realistic advantage of DV entanglement-based schemes over their CV counterparts and suggests the practical efforts for maximizing this advantage.
Discrete-variable (DV) quantum key distribution (QKD) based on single-photon detectors and sources have been successfully deployed for long-range secure key distribution. On the other hand, continuous-variable (CV) quantum key distribution (QKD) based on coherent detectors and sources is currently lagging behind in terms of loss and noise tolerance. An important discerning factor between DV-QKD and CV-QKD is the effect of phase noise, which is known to be more relevant in CV-QKD. In this article, we investigate the effect of phase noise on DV-QKD and CV-QKD protocols, including the six-state protocol and squeezed-state protocol, in a thermal-loss channel but with the assumed availability of perfect sources and detectors. We find that in the low phase noise regime but high thermal noise regime, CV-QKD can tolerate more loss compared to DV-QKD. We also compare the secret key rate as an additional metric for the performance of QKD. Requirements for this quantity to be high vastly extend the regions at which CV-QKD performs better than DV-QKD. Our analysis addresses the questions of how phase noise affects DV-QKD and CV-QKD and why the former has historically performed better in a thermal-loss channel.
Most quantum key distribution (QKD) protocols can be classified as either a discrete-variable (DV) protocol or continuous-variable (CV) protocol, based on how classical information is being encoded. We propose a protocol that combines the best of both worlds – the simplicity of quantum state preparation in DV-QKD together with the cost-effective and high-bandwidth of homodyne detectors used in CV-QKD. Our proposed protocol has two highly practical features: (1) it does not require the honest parties to share the same reference phase (as required in CV-QKD) and (2) the selection of decoding basis can be performed after measurement. We also prove the security of the proposed protocol in the asymptotic limit under the assumption of collective attacks. Our simulation suggests that the protocol is suitable for secure and high-speed practical key distribution over metropolitan distances.
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.
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.
Optical homodyne detection has been widely used in continuous-variable (CV) quantum information processing for measuring field quadrature. In this paper we explore the possibility of operating a conjugate homodyne detection system in ``photon counting'' mode to implement discrete-variable (DV) quantum key distribution (QKD). A conjugate homodyne detection system, which consists of a beam splitter followed by two optical homodyne detectors, can simultaneously measure a pair of conjugate quadratures XXX and PPP of the incoming quantum state. In classical electrodynamics, X2+P2{X}^{2}+{P}^{2}X2+P2 is proportional to the energy (the photon number) of the input light. In quantum optics, XXX and PPP do not commute and thus the above photon-number measurement is intrinsically noisy. This implies that a blind application of standard security proofs of QKD could result in pessimistic performance. We overcome this obstacle by taking advantage of two special features of the proposed detection scheme. First, the fundamental detection noise associated with vacuum fluctuations cannot be manipulated by an external adversary. Second, the ability to reconstruct the photon number distribution at the receiver's end can place additional constraints on possible attacks from the adversary. As an example, we study the security of the BB84 QKD using conjugate homodyne detection and evaluate its performance through numerical simulations. This study may open the door to a family of QKD protocols, complementary to the well-established DV-QKD based on single-photon detection and CV-QKD based on coherent detection.