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arXiv:2008.04142 · Physical Review A

Bennett-Brassard 1984 quantum key distribution using conjugate homodyne detection

Bing Qi

Published Jan 20, 2021• 24 citations
arXivHTMLPDF

Abstract

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 $X$ and $P$ of the incoming quantum state. In classical electrodynamics, ${X}^{2}+{P}^{2}$ is proportional to the energy (the photon number) of the input light. In quantum optics, $X$ and $P$ 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.

DOI
10.1103/physreva.103.012606

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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.
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.
Optical homodyne detection is widely adopted in continuous-variable quantum key distribution for high-rate field measurement quadratures. Besides that, those detection schemes have been being implemented for single-photon statistics characterization in the field of quantum tomography. In this work, we propose a discrete-variable quantum key distribution (DV-QKD) implementation that combines the use of phase modulators for high-speed state of polarization (SOP) generation, with a conjugate homodyne detection scheme which enables the deployment of high speed QKD systems. The channel discretization relies on the application of a detection threshold that allows to map the measured voltages as a click or no-click. Our scheme relies also on the use of a time-multiplexed pilot tone-quantum signal architecture which enables the use of a Bob locally generated local oscillator and opens the door to an effective polarization drift compensation scheme. Besides that, our results shows that for higher detection threshold values we obtain a very low quantum bit error rate (QBER) on the sifted key. Nevertheless, due to huge number of discarded qubits the obtained secure key length abruptly decreases. From our results, we observe that optimizing the detection threshold and considering a system operating at 500 MHz symbol generation clock, a secure key rate of approximately 46.9 Mbps, with a sifted QBER of [Formula: see text] over 40 km of optical fiber. This considering the error correction and privacy amplification steps necessary to obtain a final secure key.
Abstract In comparison to conventional discrete-variable (DV) quantum key distribution (QKD), continuous-variable (CV) QKD with homodyne/heterodyne measurements has distinct advantages of lower-cost implementation and affinity to wavelength division multiplexing. On the other hand, its continuous nature makes it harder to accommodate to practical signal processing, which is always discretized, leading to lack of complete security proofs so far. Here we propose a tight and robust method of estimating fidelity of an optical pulse to a coherent state via heterodyne measurements. We then construct a binary phase modulated CV-QKD protocol and prove its security in the finite-key-size regime against general coherent attacks, based on proof techniques of DV QKD. Such a complete security proof is indispensable for exploiting the benefits of CV QKD.
Discrete-variable quantum key distribution (DV-QKD) has recently been implemented using a homodyne detection system, and a notable secret key rate can be achieved by employing an ideal single-photon source. However, most QKD implementations employ practical light sources, including a phase-randomized weak coherent source and a heralded single-photon source, which occasionally produce multiphotons and are vulnerable to photon-number-splitting (PNS) attacks. In this work, we propose a three-decoy-state method using a heralded single-photon source for homodyne-detection-based DV-QKD, thus making it immune to PNS attacks with current technology. Our simulation results demonstrate that our proposed protocol can achieve high-speed and secure key distribution over metropolitan distances. Our work paves a cost-effective path to realize DV-QKD and further incorporate it into classical telecommunication networks.
In comparison to conventional discrete-variable (DV) quantum key distribution (QKD), continuous-variable (CV) QKD with homodyne/heterodyne measurements has distinct advantages of lower-cost implementation and affinity to wavelength division multiplexing. On the other hand, its continuous nature makes it harder to accommodate to practical signal processing, which is always discretized, leading to lack of complete security proofs so far. Here we propose a tight and robust method of estimating fidelity of an optical pulse to a coherent state via heterodyne measurements. We then construct a binary phase modulated CV-QKD protocol and prove its security in the finite-key-size regime against general coherent attacks, based on proof techniques of DV QKD. Such a complete security proof is indispensable for exploiting the benefits of CV QKD.
Quantum Key Distribution (QKD) provides a method for securely sharing a secret key between two distant parties, Alice and Bob, by leveraging the principles of quantum mechanics. This thesis focuses on Continuous-Variable (CV) QKD, a variant of QKD where information is encoded in the quadrature components of coherent light states, allowing for efficient and cost-effective detection using homodyne or heterodyne receivers. The thesis is divided into three main parts: an introduction to quantum cryptography concepts, the presentation of a CV-QKD protocol, and a detailed security proof of the protocol against different types of attacks. The security proof considers both finite and infinite symbol transmission and tackles various eavesdropping attacks, including individual, collective, and coherent attacks. The use of Gaussian states and operations provides a promising approach to enhance QKD security, particularly in the context of practical quantum cryptography. The final sections provide a mathematical framework for the optimization of secure key rates and strategies for addressing the photon-number cutoff assumption in practical implementations.