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Physical Review Applied

Quantum Key Distribution with a Continuous-Wave-Pumped Spontaneous-Parametric-Down-Conversion Heralded Single-Photon Source

Xiao-Hai Zhan, Shuang Wang, Zhen-Qiu Zhong, Zhen−Qiang Yin, Wei Chen, De‐Yong He, Guang‐Can Guo, Zheng‐Fu Han

Published Mar 8, 2023• 9 citations
Publisher

Abstract

Quantum key distribution (QKD) protocols utilize single photons for key exchanging. Heralded single-photon sources (HSPSs) with spontaneous parametric down-conversion (SPDC) is a practical and effective way of producing single photons of high fidelity, bringing extra performance especially at long distances. A pulsed laser is usually used as the pump for HSPS QKD, but it has disadvantages in operational stability and practicality compared to a cw one. On the other hand, a precise model describing the performance of HSPS with a cw pump is still missing. It is inaccurate and unsafe to apply the key rate model of the pulse-pumped HSPS QKD directly to the cw one, and it also overlooks the timing jitter and dead time of the single-photon detectors. In this paper, we study the cw case in detail, including practical imperfections of the experimental instruments. Our model shows that a cw-pumped setup can reach a much longer transmission distance (31 % longer) than the fastest pulsed HSPS QKD system at present, together with other advantages such as higher operational stability and better spectral characteristics.

DOI
10.1103/physrevapplied.19.034027

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Quantum key distribution (QKD) protocols utilize single photons for key exchanging. Heralded single-photon sources (HSPSs) with spontaneous parametric down-conversion (SPDC) is a practical and effective way of producing single photons of high fidelity, bringing extra performance especially at long distances. A pulsed laser is usually used as the pump for HSPS QKD, but it has disadvantages in operational stability and practicality compared to a cw one. On the other hand, a precise model describing the performance of HSPS with a cw pump is still missing. It is inaccurate and unsafe to apply the key rate model of the pulse-pumped HSPS QKD directly to the cw one, and it also overlooks the timing jitter and dead time of the single-photon detectors. In this paper, we study the cw case in detail, including practical imperfections of the experimental instruments. Our model shows that a cw-pumped setup can reach a much longer transmission distance (31 % longer) than the fastest pulsed HSPS QKD system at present, together with other advantages such as higher operational stability and better spectral characteristics.
Recently, a long-distance and high-key-rate quantum key distribution (QKD) has become possible by the idea of the decoy state method. We show that a longer distance QKD is possible by utilizing a heralded single-photon source (HSPS) utilizing spontaneous parametric down-conversion as a source instead of a weak coherent pulse (WCP) as proposed in the original decoy state method. Moreover, the key rate is improved by utilizing a presently available photon number resolving detector as a trigger detector of the HSPS, and it is shown to approach the key rate of the WCP.
Quantum Key Distribution (QKD) is an optical communication technique that allows two authenticated parties to exchange an encryption key using protocols grounded in the laws of quantum mechanics, making the communication intrinsically secure. A fundamental requirement for key exchange through such protocols is the use of high-performance single-photon detectors and infrared single-photon sources with low multi-photon components. In addition to the rapid progress in single-photon sources (SPSs), achieving the ideal scenario where a source emits only single photons at telecom wavelength with high efficiency remains a theoretical concept. Multi-photon components emitted by non-ideal light sources such as lasers or Spontaneous Parametric Down Conversion (SPDC) sources can open the door to successful attacks from non-legitimate parties. In this work, we demonstrate, by using a Photon-Number-Resolving Detector (PNRD), based on parallel superconducting strips, the possibility of obtaining a single-photon source with extremely multi-photon components starting from a non-single-photon light source, namely an SPDC one. To estimate the reduction of the multi-photon component, we analyzed the second-order autocorrelation function, g(2)(0), of the light source using a PNRD modelled as 8 independent pixels in parallel, in a heralding protocol. We managed to obtain a reduction of the g(2)(0) using a CW SPDC with an emission rate of about 10 MHz using several sampling bin-widths, spanning from less than one nanoseconds to hundreds of nanoseconds. These results align with the goals of the Quantum Italy Deployment project, as sources with suppressed multi-photon components could play a key role in improving the performance of QKD systems.
Weak coherent source (WCS) and spontaneous parametric down converted heralded single photon pairs have found applications in quantum key distribution (QKD) and quantum imaging (QI) experiments. Decoy state methods have also been used to enhance the security for QKD and QI. We study quantum secured imaging with the decoy state heralded single photon source (HSPS). The HSPSs superior performance in low photon number regimes makes it an ideal candidate for integrating quantum key distribution protocols to reduce measurement uncertainty and ensure secure QI. Furthermore, our results also infer the influence of the decoy state WCS, due to its higher operating speed than decoy state HSPS, would be effective in conditions that allow higher mean photon numbers for quantum secured imaging.
Mode-pairing quantum key distribution (MP-QKD) is a promising protocol immune to detector side-channel attacks and capable of breaking the repeaterless PLOB bound without global phase locking. Existing MP-QKD protocols employ weak coherent sources (WCSs) with a low probability of single-photon emission, hindering MP-QKD's performance improvement. We propose a new, to the best of our knowledge, MP-QKD protocol using the heralded single-photon source (HSPS) to significantly reduce the vacuum emission probability and increase the single-photon emission rate. Compared with the original WCS-MP-QKD protocol, this protocol has three advantages. First, its maximum transmission distance is extended from 488 km to 560 km. Second, the key rates at 100, 200, 300, and 400 km are 4.4 to 7.4 times those of the original protocol. Third, it does not change the original architecture of MP-QKD and is easy to implement experimentally. This HSPS-MP-QKD protocol has application potential in future metropolitan area QKD networks.
Entanglement-based quantum key distribution (EB-QKD) has several advantages over prepare-and-measure protocols, such as eliminating the need for decoy states and active modulators. At present, entanglement sources based on the spontaneous parametric down-conversion process have been widely used in EB-QKD experiments. Most of the existing models regard the photon-number distribution of pulse-pumped entanglement sources as thermal. However, doing so ignores any effects of spectral modes, which will lead to the overestimation of the secure key rate. In this paper, we analyze the correlation between the photon-number distribution and the joint spectral distribution and rewrite the quantum state of the photon pairs. Then we apply the results to EB-QKD and present a general model which can be used to calculate the secure key rate not only for any pulse-pumped systems but even for cw-pumped systems.
We analyze theoretically the performance of four-state quantum key distribution protocols implemented with a realistic heralded single-photon source. The analysis assumes a noisy model for the detector heralding generation of individual photons via spontaneous parametric down-conversion, including dark counts and imperfect photon number resolution. We identify characteristics of the heralding detector that defines the attainable cryptographic key rate and the maximum secure distance. Approximate analytical formulas are applied to multiplexed detection and compared with results of numerical calculations.