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arXiv:quant-ph/0508099 · Physical Review A

Photon-number-resolving decoy-state quantum key distribution

Qing-yu Cai, Yong-Gang Tan

Published Mar 3, 2006• 41 citations
arXivHTMLPDF

Abstract

In this paper, a photon-number-resolving decoy-state quantum key distribution (QKD) scheme is presented based on recent experimental advancements. A new upper bound on the fraction of counts caused by multiphoton pulses is given, which seems inherent as long as weak coherent sources and high lossy channel are used. This implies that our scheme is optimal in long-distance QKD with weak coherent sources. We show that Eve's coherent multiphoton pulse (CMP) attack is more efficient than a symmetric individual attack when the quantum bit error rate is small, so that the CMP attack should be considered to ensure the security of the final key. Our results show that a not-so-weak pulse can be used to transmit the key. Optimal intensity of the laser source is presented which provides a $23.9\phantom{\rule{0.3em}{0ex}}\mathrm{km}$ increase in the transmission distance.

DOI
10.1103/physreva.73.032305

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In this paper, a photon-number-resolving decoy-state quantum key distribution (QKD) scheme is presented based on recent experimental advancements. A new upper bound on the fraction of counts caused by multiphoton pulses is given, which seems inherent as long as weak coherent sources and high lossy channel are used. This implies that our scheme is optimal in long-distance QKD with weak coherent sources. We show that Eve's coherent multiphoton pulse (CMP) attack is more efficient than a symmetric individual attack when the quantum bit error rate is small, so that the CMP attack should be considered to ensure the security of the final key. Our results show that a not-so-weak pulse can be used to transmit the key. Optimal intensity of the laser source is presented which provides a 23.9km23.9\phantom{\rule{0.3em}{0ex}}\mathrm{km}23.9km increase in the transmission distance.
With the potential of quantum computers to compromise current public-key cryptosystems, Quantum Key Distribution (QKD), which is based on the physical laws of quantum mechanics, has garnered significant attention. However, while QKD security proofs typically assume ideal single-photon sources, realistic implementations rely on Weak Coherent Pulses (WCP) due to the difficulties associated with commercializing true single-photon sources. Unfortunately, the multi-photon components inherent in WCPs are vulnerable to Photon Number Splitting (PNS) attacks, which limits the secure transmission distance to a few tens of kilometers. This article introduces the Decoy State method, which effectively resolves this issue. Proposed by W.-Y. Hwang in 2003 and further advanced by H.-K. Lo and X.-B. Wang, this technique utilizes the random interleaving of pulses with different mean photon numbers during transmission. By doing so, it enables the accurate estimation of single-photon yield and error rates, thereby effectively detecting PNS attacks. Because it can be implemented using standard commercial lasers and intensity modulators, the Decoy State method has become the standard technology in most modern QKD systems. It serves as a core component for long-distance quantum communication, enabling major milestones reported recently. This article reviews the principles, mathematical analysis, and latest applications of the Decoy State method.
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.
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 (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 heralded single photon source and it is shown to approach the key rate of the WCP.
The passive decoy scheme represents a quantum key distribution protocol that employs a photon number resolving detector to selectively extract the decoy states from the signal states during post-processing. This selection process ensures resilience against attacks capable of distinguishing between these two states, thereby enhancing the security of the protocol. Previous research has emphasized the good performance of the protocol under optimal conditions. However, our study focuses on numerically evaluating the protocol performance in various practical scenarios. We aim to understand the implications of these scenarios in terms of the maximum attainable attenuation and bit rate per second, considering the number of photons per pulse sent under specific experimental conditions. Our findings demonstrate that opting for a low average photon number value ensures high tolerance to attenuation during communication, albeit at the cost of a reduced bit rate per second. Conversely, for lower attenuations, it is more advantageous to increase the average number of photons, even if it deviates from the ideal behaviour of a single-photon source. The benefit of selecting the decoy states at the end of the transmission remains consistent across different configurations. This research signifies an advancement in assessing the viability of incorporating the protocol within a practical QKD network.
To increase the security distance of quantum communication,a new scheme of decoy state quantum key distribution with a modified coherent state is proposed.The probability of multi-photon pulse in weak coherent source can be decreased by canceling two photon pulses to improve the security distance.Based on the math model of the decoy state QKD,the formula for the yield and error rate of the single photon pulse with the Modified Coherent State is deduced,and substituted in GLLP to calculate the generation rate of quantum keys.Results show that the decoy state with the Modified Coherent State can increase the secure communication distance about 10%,which is very close to that of the perfect decoy state QKD.
We propose an efficient method to verify the upper bound of the fraction of counts caused by multiphoton pulses in practical quantum key distribution using weak coherent light, given whatever type of Eve's action. The protocol simply uses two coherent states for the signal pulses and vacuum for the decoy pulse. Our verified upper bound is sufficiently tight for quantum key distribution with a very lossy channel, in both the asymptotic and nonasymptotic case. So far our protocol is the only decoy-state protocol that works efficiently for currently existing setups.