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Physical Review A

Limitation of decoy-state Scarani-Acin-Ribordy-Gisin quantum-key-distribution protocols with a heralded single-photon source

ShengLi Zhang, Xu‐Bo Zou, Ke Li, Chenhui Jin, Guang‐Can Guo

Published Oct 8, 2007• 13 citations
Publisher

Abstract

For the Bennett-Brassard 1984 (BB84) quantum key distribution, longer distance and higher key generating rate is shown with a heralded single-photon source (HSPS) [Phys. Rev. A. 73, 032331 (2006)]. In this paper, the performance of the Scarani-Acin-Ribordy-Gisim (SARG) protocol utilizing the HSPS sources is considered and the numerical simulation turns out that still a significant improvement in secret key generating rate can also be observed. It is shown that the security distance for $\mathrm{HSPS}+\mathrm{SARG}$ is $120\phantom{\rule{0.3em}{0ex}}\mathrm{km}$. However, compared with the $\mathrm{HSPS}+\mathrm{BB}84$ protocols, the $\mathrm{HSPS}+\mathrm{SARG}$ protocol has a lower secret key rate and a shorter distance. Thus we show the $\mathrm{HSPS}+\mathrm{BB}84$ implementation is a preferable protocol for long distance transmittance.

DOI
10.1103/physreva.76.044304

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For the Bennett-Brassard 1984 (BB84) quantum key distribution, longer distance and higher key generating rate is shown with a heralded single-photon source (HSPS) [Phys. Rev. A. 73, 032331 (2006)]. In this paper, the performance of the Scarani-Acin-Ribordy-Gisim (SARG) protocol utilizing the HSPS sources is considered and the numerical simulation turns out that still a significant improvement in secret key generating rate can also be observed. It is shown that the security distance for HSPS+SARG\mathrm{HSPS}+\mathrm{SARG}HSPS+SARG is 120km120\phantom{\rule{0.3em}{0ex}}\mathrm{km}120km. However, compared with the HSPS+BB84\mathrm{HSPS}+\mathrm{BB}84HSPS+BB84 protocols, the HSPS+SARG\mathrm{HSPS}+\mathrm{SARG}HSPS+SARG protocol has a lower secret key rate and a shorter distance. Thus we show the HSPS+BB84\mathrm{HSPS}+\mathrm{BB}84HSPS+BB84 implementation is a preferable protocol for long distance transmittance.
The Scarani-Acin-Ribordy-Gisin 2004 (SARG04) protocol was proposed by V. Scarani et al. In this paper, the performance of SARG04 protocols utilizing weak coherent state (WCS) and heralded single photon source (HSPS) are investigated, and the influence of decoy-state idea on SARG04 protocol is analyzed. Furthermore, the choice of optimal signal intensity for SARG04 protocol is discussed and the condition that the optimal signal intensity satisfies is obtained. The simulation and analysis results show that SARG04 protocol with WCS has the best key generation rate and transmission distance (88 km) comparing with SARG04 protocol with HSPS, BB84 protocol with WCS or HSPS. The decoy state method can substantially prolong the secure distance of SARG04 protocol to 165 km with WCS and 173 km with HSPS, and the performance of decoy-state SARG04 protocol is better than that of decoy-state BB84 protocol. The decoy state method weakens the dependence of the optimal signal intensity on the overall transmission probability.
We compare the performance of Bennett-Brassard 1984 (BB84) and Scarani-Acin-Ribordy-Gisin 2004 (SARG04) protocols, the latter of which was proposed by V. Scarani et al. [Phys. Rev. Lett. 92, 057901 (2004)]. Specifically, in this paper, we investigate the SARG04 protocol with two-way classical communications and the SARG04 protocol with decoy states. In the first part of the paper, we show that the SARG04 scheme with two-way communications can tolerate a higher bit error rate (19.4% for a one-photon source and 6.56% for a two-photon source) than the SARG04 one with one-way communications (10.95% for a one-photon source and 2.71% for a two-photon source). Also, the upper bounds on the bit error rate for the SARG04 protocol with two-way communications are computed in a closed form by considering an individual attack based on a general measurement. In the second part of the paper, we propose employing the idea of decoy states in the SARG04 scheme to obtain unconditional security even when realistic devices are used. We compare the performance of the SARG04 protocol with decoy states and the BB84 one with decoy states. We find that the optimal mean-photon number for the SARG04 scheme is higher than that of the BB84 one when the bit error rate is small. Also, we observe that the SARG04 protocol does not achieve a longer secure distance and a higher key generation rate than the BB84 one, assuming a typical experimental parameter set.
Decoy states have recently been proposed as a useful method for substantially improving the performance of quantum key distribution (QKD). Considering the Scarani-Acin-Ribordy-Gisin protocol (SARG04) with a heralded single photon source (HSPS), we review the general model of HSPS QKD system with a threshold detector, and analyze the SARG04 non-decoy-state protocol, SARG04 infinite active decoy-state protocol and SARG04 decoy-state protocol combining active decoy state method and passive decoy state method. Furthermore, we discuss the choice of optimal signal intensity for HSPS QKD with and without decoy states and obtain the condition that the optimal signal intensity satisfies. The simulation and analysis results show that the decoy state method can substantially improve the performance of SARG04 protocol with HSPS and the performance of SARG04 protocol with HSPS is better than that of BB84 protocol with HSPS. The decoy state method weakens the dependence of the optimal signal intensity on the overall transmission probability.
For the Bennett-Brassard 1984 (BB84) quantum key distribution, longer distance and higher key generation rate is shown with a heralded single photon source (HSPS). In this paper, the nonorthogonal encoding protocol SARG04 based on one vacuum and two weak decoy states with HSPS is presented. According to the public announcement of Alice's detection events, the overall gain of Bob's detector and quantum bit error rate (QBER) can be divided into two groups, triggered components and nontriggered components. We present a new protocol that use both triggered and nontriggered components to estimate the fraction and QBER of single-photon and two-photon pulses, and then deduce the final secure key generation rate. The final key generation rate over transmission distance is simulated, which shows that we can obtain a higher key rate than that of the existing methods.
Recently the performance of the quantum key distribution (QKD) is substantially improved by the decoy state method and the non-orthogonal encoding protocol, separately. In this paper, a practical non-orthogonal decoy state protocol with a heralded single photon source (HSPS) for QKD is presented. The protocol is based on 4 states with different intensities, i.e. one signal state and three decoy states. The signal state is for generating keys; the decoy states are for detecting the eavesdropping and estimating the fraction of single-photon and two-photon pulses. We have discussed three cases of this protocol, i.e. the general case, the optimal case and the special case. Moreover, the final key rate over transmission distance is simulated. For the low dark count of the HSPS and the utilization of the two-photon pulses, our protocol has a higher key rate and a longer transmission distance than any other decoy state protocol.
Twin-field quantum key distribution (TF-QKD) can overcome the fundamental rate-loss limit in the point-to-point QKD without a quantum repeater and achieve high key rates over long distances. However, TF-QKD protocol and its variants commonly use weak coherent pulses (WCPs) as light sources. The vacuum part of WCP accounts for a large proportion, resulting in the lower photon detection rate of the communication receiver, which leads to a shorter transmission distance of the secret key. In this paper, we propose an active-decoy TF-QKD protocol with heralded single-photon source (HSPS), which can achieve higher key rate and longer transmission distance than the active-decoy TF-QKD protocol with WCPs. Also, in order to resist the side channel attacks caused by actively modulating intensity of the pulses, we propose a passive-decoy TF-QKD protocol with HSPS to enhance the security, which can perform almost as good as the active-decoy TF-QKD protocol with WCPs.