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arXiv:quant-ph/0504221

Optimal Experimental Scheme for Bennett-Brassard 1984 Quantum Key Distribution Protocol with Weak Coherent Sources, Noisy and Lossy Channel

Qing-yu Cai

Published Apr 29, 2005• 0 citations
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Abstract

It is the first scheme which allows the detection apparatus to achieve both the photon number of arriving signals and quantum bit error rate of the multiphoton pulses precisely. We show that the upper bound of the fraction of the tagged multiphoton pulses counts is $μ$, which is independent of the channel loss and the intensity of the decoy source. Such upper bound is $inherent$ and cannot be reduced any longer as long as the weak coherent scouces and high lossy channel are used. We show that our scheme can be implemented even if the channel loss is very high. A stronger intensity of the pulse source is allowable to improve the rate of quantum key distribution. Both the signal pulses and decoy pulses can be used to generate the raw key after verified the security of the communication. We analyze that our scheme is optimal under today's technology. PACS: 03.67.Dd

DOI
10.48550/arxiv.quant-ph/0504221

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It is the first scheme which allows the detection apparatus to achieve both the photon number of arriving signals and quantum bit error rate of the multiphoton pulses precisely. We show that the upper bound of the fraction of the tagged multiphoton pulses counts is μμμ, which is independent of the channel loss and the intensity of the decoy source. Such upper bound is inherentinherentinherent and cannot be reduced any longer as long as the weak coherent scouces and high lossy channel are used. We show that our scheme can be implemented even if the channel loss is very high. A stronger intensity of the pulse source is allowable to improve the rate of quantum key distribution. Both the signal pulses and decoy pulses can be used to generate the raw key after verified the security of the communication. We analyze that our scheme is optimal under today's technology. PACS: 03.67.Dd
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.
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.
We propose a decoy-pulse method to overcome the photon-number-splitting attack for Bennett-Brassard 1984 quantum key distribution protocol in the presence of high loss: A legitimate user intentionally and randomly replaces signal pulses by multiphoton pulses (decoy pulses). Then they check the loss of the decoy pulses. If the loss of the decoy pulses is abnormally less than that of signal pulses, the whole protocol is aborted. Otherwise, to continue the protocol, they estimate the loss of signal multiphoton pulses based on that of decoy pulses. This estimation can be done with an assumption that the two losses have similar values. We justify that assumption.
We apply the techniques introduced by Kraus et al. [Phys. Rev. Lett. 95, 080501 (2005)] to prove security of quantum-key-distribution (QKD) schemes using two-way classical post-processing as well as QKD schemes based on weak coherent pulses instead of single-photon pulses. As a result, we obtain improved bounds on the secret-key rate of these schemes. For instance, for the six-state protocol using two-way classical post-processing we recover the known threshold for the maximum tolerated bit error rate of the channel, 0.276, but demonstrate that the secret-key rate can be substantially higher than previously shown. Moreover, we provide a detailed analysis of the Bennett-Brassard 1984 (BB84) and the SARG protocol using weak coherent pulses (with and without decoy states) in the so-called untrusted-device scenario, where the adversary might influence the detector efficiencies. We evaluate lower bounds on the secret-key rate for realistic channel parameters and show that, for channels with low noise level, the bounds for the SARG protocol are superior to those for the BB84 protocol, whereas this advantage disappears with increasing noise level.
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The performance of a practical quantum key distribution (QKD) system is often limited by the multi-photon state emission of its source and the dark counts of its detectors. Here, we present two methods to improve its performance. The first method is decoy state QKD: the sender randomly sends out weak coherent states with various average photon numbers (which are named as signal state and decoy states). In [14,15], we have performed the first experimental implementation of decoy state QKD over 15km and 60km respectively, thus dramatically increasing the distance and secure key generation rate of practical QKD systems. Our work has been followed up by many research groups worldwide [16-18]. The second scheme is QKD with "dual detectors" [19]: the legitimate receiver randomly uses either a fast (but noisy) detector or a quiet (but slow) detector to measure the incoming quantum signals. The measurement results from the quiet detector can be used to upper bound the eavesdropper's information, while the measurement results from the fast detector are used to generate a secure key. We applied this idea to various QKD protocols. Simulation results demonstrated significant improvements in both BB84 protocol with ideal single photon source and Gaussian-modulated coherent states protocol.