We propose a family of sifting-less quantum-key-distribution protocols which use reverse reconciliation, and are based on weak coherent pulses (WCPs) polarized along
m different directions. When
m=4, the physical part of the protocol is identical to most experimental implementations of BB84 [Bennett and Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, New York, 1984)] and SARG04 [Scarani, Ac\'{\i}n, Ribordy, and Gisin, Phys. Rev. Lett. 92, 057901 (2004); Ac\'{\i}n, Gisin, and Scarani, Phys. Rev. A 69, 012309 (2004)] protocols and they differ only in classical communications and data processing. We compute their total key rate as a function of the channel transmission
T, using general information theoretical arguments, and we show that they have a higher key rate than the more standard protocols, both for fixed and optimized average photon number of the WCPs. When no decoy-state protocols (DSPs) [Hwang, Phys. Rev. Lett. 91, 057901 (2003); Lo, Ma, and Chen, Phys. Rev. Lett. 94, 230504 (2005); Wang, Phys. Rev. A 72, 012322 (2005)] are applied, the scaling of the key rate with transmission is improved from
T2 for BB84 to ${T}^{1+\frac{1}{m\ensuremath{-}2}}$. If a DSP is applied, we show how the key rates scale linearly with
T, with an improvement of the prefactor by 75.96% for
m=4. High values of
m allow one to asymptotically approach the key rate obtained with ideal single-photon pulses. The fact that the key rates of these sifting-less protocols are higher compared to those of the aforementioned more standard protocols show that the latter are not optimal, since they do not extract all the available secret keys from the experimental correlations.
Quantum key distribution with the Bennett-Brassard 1984 protocol has been shown to be unconditionally secure even using weak coherent pulses instead of single-photon signals. The distances that can be covered by these methods are limited due to the loss in the quantum channel (e.g., loss in the optical fiber) and in the single-photon counters of the receivers. One can argue that the loss in the detectors cannot be changed by an eavesdropper in order to increase the covered distance. Here we show that the security analysis of this scenario is not as easy as is commonly assumed, since already two-photon processes allow eavesdropping strategies that outperform the known photon-number splitting attack. For this reason there is, so far, no satisfactory security analysis available in the framework of individual attacks.
We propose a family of sifting-less quantum-key-distribution protocols which use reverse-reconciliation, and are based on weak coherent pulses (WCPs) polarized along m different directions. When m=4, the physical part of the protocol is identical to most experimental implementations of BB84 and SARG04 protocols and they differ only in classical communications and data processing. We compute their total keyrate as function of the channel transmission T, using general information theoretical arguments and we show that they have a higher keyrate than the more standard protocols, both for fixed and optimized average photon number of the WCPs. When no decoy-state protocols (DSPs) are applied, the scaling of the keyrate with transmission is improved from T2 for BB84 to T^(1+1/(m-2)). If a DSP is applied, we show how the keyrates scale linearly with T, with an improvement of the prefactor by 75.96 % for m=4. High values of $ m $ allow to asymptotically approach the keyrate obtained with ideal single photon pulses. The fact that the keyrates of these sifting-less protocols are higher compared to those of the aforementioned more standard protocols show that the latter are not optimal, since they do not extract all the available secret key from the experimental correlations.
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
This paper presents an investigation of practical quantum secure communication using multi-photon tolerant protocols. Multi-photon tolerant protocols loosen the limit on the number of photons imposed by currently used quantum key distribution protocols. The multi-photon tolerant protocols investigated in this paper are multi-stage protocols that do not require any prior agreement between a sender Alice and a receiver Bob. The security of such protocols stems from the fact that the optimal detection strategies between the legitimate users and the eavesdropper are asymmetrical, allowing Bob to obtain measurement results deterministically while imposing unavoidable quantum noise to the eavesdropper Eve's measurement. Multi-photon tolerant protocols are based on the use of transformations known only to the communicating party applying them i.e. either Alice or Bob. In this paper multi-photon tolerant protocols are used in order to share a key or a message between a sender Alice and a receiver Bob. Thus such protocols can be either used as quantum key distribution (QKD) protocols or quantum communication protocols. In addition, multi-stage protocols can be used to share a key between Alice and Bob, followed by the shared key used as a seed key to a single-stage protocol, called the braiding concept. This paper presents a practical study of multi-photon tolerant multi-stage protocols. Security aspects as well as challenges to the practical implementation are discussed. In addition, secret raw key generation rates are calculated with respect to both losses and distances over a fiber optical channel. It is well-known that raw key generation rates decreases with the increase in channel losses and distances. In this paper, coherent non-decoying quantum states are used to transfer the encoded bits from Alice to Bob. Raw key generation rates are calculated for different average photon numbers µ and compared with the case of µ=0.1, which is the average number of photons used in most single-photon based QKD protocols. Furthermore, an optimal average number of photons to be used within the secure region of the multi-photon tolerant protocols is calculated. It is worth noting that, with the increased key generation rates and distances of communication offered by the multi-photon tolerant protocols, quantum secure communication need not be restricted to quantum key distribution; it can be elevated to attain direct quantum secure communication.
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.